I think the logic behind this argument is actually much, much simpler.

Let us suppose that consciousness is not a type of computation.

Rational argument, and hence rational description IS a type of computation - it can be made into forms that are computable.

Therefore consciousness, if it is not a type of computation, is also not describeable within, or reducible to, rational argument.

I call this type of thing the para-rational - it's not necessarily against rationality to suppose that something exists which isn't rationally describable. What doesn't make sense is to go on to either

a) Attempt to rationally describe it in detail afterwards. or b) Use it as an excuse to avoid thinking rationally about things you CAN think about in a rational way. c) Try and use its properties in a logical argument - all this gives you on the whole is an illogical argument.

So yes, there might be an aspect of consciousness which is beyond the rational, and which is always associated with certain types of existent being. But I would prefer the proposition that this is para-rational - alongside the rational realm, rather than irrational - joined to the rational realm, and making it non-rational after all.

This is a difficult area - as one should necessarily believe para-rational things for para-rational reasons (whatever THAT means). But I can't see how we could rule out other types of 'existence'. However, I can see good reasons not to make it a subject of too much rational discussion - if you can't rationally describe something, don't attempt to....