Physically, yes of course they can remove your engine and swap in a different one without telling you. It's also highly illegal. Engine number will be recorded on the registration, and any change to that number has to get updated with the RTA/RMS.
Sounds like you're just being paranoid, a lot of smash repair places are quite busy and cars will sit there for a while until they get fixed. Also, has your insurance assessor gone over the car yet? Maybe they're waiting on that to happen (and insurance agents are often lazier than smashies, especially if they are going to have to pay out)
Also, this doesn't belong in the "86 Club" section....