Personnaly I would never use such a drug. I conceptualise myself as a tought-based kernel with a bunch of meat around to make it run. This kernel tries hardly to think about itself as 'one thing' (you don't achieve much with schizophrenia), and that relies heavily on this kernel being able to trace a continuous stream of tought back to its birth (at least as far as it can remember). Alter this stream and you loose yourself (the bigger the altering the bigger the loosing).
Two more things: (i) I'm aware that not everybody thinks the same, mainly because fellow humans acts as a constant reminder of who you were before, and (ii) yes, sleeping is disturbing to me, I try not to think about it too much.
What's your opinion on the common teleportation dilemma? If there were a machine, that would instantly destroy my body and assemble it somewhere else (even from completely different atoms) so that from my point of view, I instantly vanish and appear elsewhere, does this count as interruption to my line of consciousness? Doesn't really seem like it to me. After all, my memories and thoughts are stored in the patterns of matter and those are preserved.
Teleportation isn't very concerning to me, because it's basically against known physic rules for now on. Theoretically I would be very wary of teleportation, on a pragmatic level: if I don't own the teleportation process on an extreme level then there's too much risk to be altered in some (maybe dramatic) way.
However, there's a variant that sucks my thoughts sometimes: what about transferring a full brain's backup into a valid recipient?
Classical application would be life extension: going into a "blank" body/brain (or big enough computer) when mine is too old to carry on. It's still very inconceivable nowadays, but much more attainable than teleportation I think.
You can't "switch off" the old brain, copy it, and "switch on" the new one, because that would pose the same questions as teleportation. Neither I wouldn't start a copy process, wait for it to complete, commit suicide and set alive the new body/brain in the same time.
The obvious solution would be to find a way to connect two brains (be it an organically or computerized brain), extend the thought in such a way that there would be full redundancy of memories between the two devices, and the switch off the old one.
Two more things: (i) I'm aware that not everybody thinks the same, mainly because fellow humans acts as a constant reminder of who you were before, and (ii) yes, sleeping is disturbing to me, I try not to think about it too much.