Definitely. Assume EVERYTHING you do on that computer is fully known to your employer. It doesn't matter if they say they can't see it, that's bullshit. Don't take their word for a damn thing, and don't rely on contracts, privacy policies or similar "paper" to protect you because you'll only know if it works _after_ you've been exploited and likely suffered the consequences.

I keep my employer's laptop off, lid shut, on the other side of the room, disconnected from power. I just use my own and tell them otherwise. 8 months and they haven't noticed (yet). If/when they do I'll just set it up to remote in from my real computer and practice some very hardcore discipline.