Yes, they will die, assuming a few circumstances. Here I'm assuming you have some number of drillers, some number of captive specialists, and your own Assassin sitting at an outpost before an enemy sub arrives.
The order will be:
- All specialists at the outpost with priority < 6 have their effects trigger (including your enemies').
- You assassin kills all specialists at the outpost which aren't yours (assuming no enemy Revered Elders).
- All specialists with priority > 6 have their effects trigger (if they haven't been killed yet).
- Shields are applied.
- Driller combat ensues.
- Outpost ownership is determined.
Note that if the specialist you have captive has a priority < 6, it may be a good idea to release them so that they aren't in combat at that outpost and have to wait a return trip to be useful to your opponent. For example, if the specialist is a Thief or Infiltrator, it could mean the difference between holding, or losing control of the outpost.
While combat is happening, ownership of an outpost is being contested, and all present specialists are considered.