No, I would never expect to simultaneously experience being on both Mars and Earth. If you find anyone who believes that, they are severely confused, or are trolling you.
If I know the replicator will get stuck and output 99 dentins on Mars, I would only expect a 1% chance of waking up on earth. If I'm told that it will only output one copy, I would expect a 50% chance of waking up on earth, only to find out later that the actual probability was 1%. The map is not the territory.
Further, doesn't it seem odd that you are assigning any probability that after a non-invasive scan, and while your brain and body continues to operate just fine on Earth, you suddenly find yourself on Mars, and someone else takes over your life on Earth?
Not at all. In fact, it seems odd to me that anyone would be surprised to end up on Mars.
What is the mechanism by which you expect your subjective experience to be transferred from Earth to Mars?
Because conciousness is how information processing feels from the inside, and 'information processing' has no intrinsic requirement that the substrate or cycle times be continuous.
If I pause a playing wave file, copy the remainder to another machine, and start playing it out, it still plays music. It doesn't matter that the machine is different, that the decoder software is different, that the audio transducers are different - the music is still there.
Another, closer analogy is that of the common VM: it is possible to stop a VPS (virtual private server), including operating system, virtual disk, and all running programs, take a snapshot, copy it entirely to another machine halfway around the planet, and restart it on that other machine as though there were no interruption in processing. The VPS may not even know that anything has happened, other than suddenly its clock is wrong compared to external sources. The fact that it spent half an hour 'suspended' doesn't affect its ability to process information one whit.
Background:
On the most recent LessWrong readership survey, I assigned a probability of 0.30 on the cryonics question. I had previously been persuaded to sign up for cryonics by reading the sequences, but this thread and particularly this comment lowered my estimate of the chances of cryonics working considerably. Also relevant from the same thread was ciphergoth's comment:
Based on this, I think there's a substantial chance that there's information out there that would convince me that the folks who dismiss cryonics as pseudoscience are essentially correct, that the right answer to the survey question was epsilon. I've seen what seem like convincing objections to cryonics, and it seems possible that an expanded version of those arguments, with full references and replies to pro-cryonics arguments, would convince me. Or someone could just go to the trouble of showing that a large majority of cryobiologists really do think cryopreserved people are information-theoretically dead.
However, it's not clear to me how well worth my time it is to seek out such information. It seems coming up with decisive information would be hard, especially since e.g. ciphergoth has put a lot of energy into trying to figure out what the experts think about cryonics and come away without a clear answer. And part of the reason I signed up for cryonics in the first place is because it doesn't cost me much: the largest component is the life insurance for funding, only $50 / month.
So I've decided to put a bounty on being persuaded to cancel my cryonics subscription. If no one succeeds in convincing me, it costs me nothing, and if someone does succeed in convincing me the cost is less than the cost of being signed up for cryonics for a year. And yes, I'm aware that providing one-sided financial incentives like this requires me to take the fact that I've done this into account when evaluating anti-cryonics arguments, and apply extra scrutiny to them.
Note that there are several issues that ultimately go in to whether you should sign up for cryonics (the neuroscience / evaluation of current technology, estimate of the probability of a "good" future, various philosophical issues), I anticipate the greatest chance of being persuaded from scientific arguments. In particular, I find questions about personal identity and consciousness of uploads made from preserved brains confusing, but think there are very few people in the world, if any, who are likely to have much chance of getting me un-confused about those issues. The offer is blind to the exact nature of the arguments given, but I mostly foresee being persuaded by the neuroscience arguments.
And of course, I'm happy to listen to people tell me why the anti-cryonics arguments are wrong and I should stay signed up for cryonics. There's just no prize for doing so.