Could the crew of an Alcubierre drive-equipped spaceship avoid getting cooked alive by hawking radiation if their spaceship engaged and disengaged warp speed periodically over short distances?
Do warp drives produce radiation? How much? Do small warps produce less?
Physicists agree: We have absolutely no idea.
Compared to the many unknown problems of an Alcubierre drive, dealing with radiation is a solved problem in general. You need either:
- to not care about damages
A layer of lead sufficiently many light years thick is known to stop known forms of radiation. Similarly, all forms or radiation diminish by the square of the distance to the source (although Alcubierre drives do funky things to spacetime).
You could interpret 3) in a number of different ways, but strategies like "storing the crew's brains in a computer and build them new bodies after radiation destroys the original ones" are completely compatible with our current understanding of physics.
When dealing with exotic matter twisting space time and potentially being a time machine and requiring new physics, worrying about radiation is a trivial matter.