My opinion, admittedly based on limited experience:
Can you shock an autoflower by transplanting? Answer, yes.
Can most, if not all autoflowers be "transplanted" into a larger pot? Also yes, I think, although perhaps not strains that I have not worked with.
In my opinion, most transplant shock (I did not say all) is technique. I have "transplanted" every plant I have grown to one degree or another, and have yet to see recognizable problems as a result. In every case, healthy growth continued within a day or two. I think there are two issues that need dealing with. First, the osmotic environment needs to be consistent. Same or similar medium, and same EC level of nutes. If you move a seedling from where they are experiencing a ~500EC environment and hit them with no nutes, or a completely different EC level, or perhaps, significantly different nutes at a similar EC, this stresses the plant because it will take time for it to adjust root function to adapt to the new osmotic conditions, and/or nute mix. My rule is same EC, same nutes in the new pot as in the old.
The second issue is root damage, which can be hard to avoid especially if transplanting occurs before the roots have tied the medium in the small pot together, which is the norm in my grows. I deal with this by making transplant cups which allow removing the bottom before putting the rest of the pot with the plant in it into a hole shaped to fit, and then removing the sides of the pot (already split on two sides) by lifting the sides out of the hole leaving the plant in place with a minimally disturbed root and medium ball. So far, the combination of transplant cups and managing EC levels carefully have had 100% success for me. One of these days I will run into a plant that really doesn't like what I do, but so far, I have not.
Happy transplanting.