Yes, they can. Units are always allowed to attack, until they are removed from the board at the end of the activation phase. 

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Removing casualties: Influence markers killed during the attack are removed
immediately. Special units killed during the attack are removed AFTER all attacks
have been performed by all players for that turn. Special units can always perform
their attacks, even if they were killed by another player earlier in that turn
( It is recommended to place the special unit on its side after a defeat to indicate
that it has already been killed that turn).
The killed influence markers and units are always returned to their owners after
all attacks have been resolved.