No, the distinction between MWI and Copenhagen would have actual physical consequences. For instance, if you die in the Copenhagen interpretation, you die in real life. If you die in MWI, there is still a copy of you elsewhere that didn't die. MWI allows for quantum immortality.
Analogously, under the A-theory, dying-you does not exist anywhere in spacetime. The only "you" that exists is the present living you.
Under the B-theory, dying-you does exist right now (assuming that you'll eventually die). It just doesn't exist (I hope) at this point in spacetime, where "this point" is the point at which you are reading this sentence. When you die in the A-theory, there is not a copy of you elsewhen that isn't dying. The B-theory, in contrast, allows for a kind of Spinoza-style timeless immortality. It will always be the case that you are living at this moment.
(As usual in this thread, I'm treating "A-theory" and "presentism" as being broadly synonymous.)
If you think that other points of spacetime exist, then you're essentially a B-theorist. If you want to be an A-theorist nonetheless, you'll have to add some kind of additional structure to your world model, just as single-world QM needs to add a "world eater" to many-worlds QM.
I'm not entirely sure what you mean by 'Spinoza-style', but I get the gist of it and find this analogy interesting. Could you explain what you mean by Spinoza-style? My knowledge of ancient philosophers is a little rusty.
I've always been puzzled by why so many people have such strong intuitions about whether the A-theory or the B-theory1 of time is true. [ETA: I've written "A-theory" and "B-theory" as code for "presentism" and "eternalism", but see the first footnote.] It seems like nothing psychologically important turns on this question. And yet, people often have a very strong intuition supporting one theory over the other. Moreover, this intuition seems to be remarkably primitive. That is, whichever theory you prefer, you probably felt an immediate affinity for that conception of time as soon as you started thinking about time at all. The intuition that time is A-theoretic or B-theoretic seems pre-philosophical, whichever intuition you have. This intuition will then shape your subsequent theoretical speculations about time, rather than vice-verse.
Consider, by way of contrast, intuitions about God. People often have a strong pre-theoretical intuition about whether God exists. But it is easy to imagine how someone could form a strong emotional attachment to the existence of God early in life. Can emotional significance explain why people have deeply felt intuitions about time? It seems like the nature of time should be emotionally neutral2.
Now, strong intuitions about emotionally neutral topics aren't so uncommon. For example, we have strong intuitions about how addition behaves for large integers. But usually, it seems, such intuitions are nearly unanimous and can be attributed to our common biological or cultural heritage. Strong disagreeing intuitions about neutral topics seem rarer.
Speaking for myself, the B-theory has always seemed just obviously true. I can't really make coherent sense out of the A-theory. If I had never encountered the A-theory, the idea that time might work like that would not have occurred to me. Nonetheless, at the risk of being rude, I am going to speculate about how A-theorists got that way. (B-theorists, of course, just follow the evidence ;).)
I wonder if the real psycho-philosophical root of the A-theory is the following. If you feel strongly committed to the A-theory, maybe you are being pushed into that position by two conflicting intuitions about your own personal identity.
Intuition 1: On the one hand, you have a notion of personal identity according to which you are just whatever is accessible to your self-awareness right now, plus maybe whatever metaphysical "supporting machinery" allows you to have this kind of self-awareness.
Intuition 2: On the other hand, you feel that you must identify yourself, in some sense, with you-tomorrow. Otherwise, you can give no "rational" account of the particular way in which you care about and feel responsible for this particular tomorrow-person, as opposed to Brittany-Spears-tomorrow, say.
But now you have a problem. It seems that if you take this second intuition seriously, then the first intuition implies that the experiences of you-tomorrow should be accessible to you-now. Obviously, this is not the case. You-tomorrow will have some particular contents of self-awareness, but those contents aren't accessible to you-now. Indeed, entirely different contents completely fill your awareness now — contents which will not be accessible in this direct and immediate way to you-tomorrow.
So, to hold onto both intuitions, you must somehow block the inference made in the previous paragraph. One way to do this is to go through the following sequence:
One potential problem with this psychological explanation is that it doesn't explain the significance of "becoming". Some A-theorists report that a particular basic experience of "becoming" is the immediate reason for their attachment to the A-theory. But the story above doesn't really have anything to do with "becoming", at least not obviously. (This is because I can't make heads or tails of "becoming".)
Second, intuitions about time, even in their primitive pre-reflective state, are intuitions about everything in time. Yet the story above is exclusively about oneself in time. It seems that it would require something more to pass from intuitions about oneself in time to intuitions about how the entire universe is in time.
1 [ETA: In this post, I use the words "A-theory" and "B-theory" as a sloppy shorthand for "presentism" and "eternalism", respectively. The point is that these are theories of ontology ("Does the future exist?"), and not just theories about how we should talk about time. This shouldn't seem like merely a semantic or vacuous dispute unless, as in certain caricatures of logical positivism, you think that the question of whether X exists is always just the question of whether X can be directly experienced.]
2 Some people do seem to be attached to the A-theory because they think that the B-theory takes away their free will by implying that what they will choose is already the case right now. This might explain the emotional significance of the A-theory of time for some people. But many A-theorists are happy to grant, say, that God already knows what they will do. I'm trying to understand those A-theorists who aren't bothered by the implications of the B-theory for free will.