You should always give notice, if at all possible. It's the right and professional thing to do and can only help you.
This^^^. Keep notes as to how it all shakes out...just to CYA.
Even if you give notice, they may show you the door anyway. So be it...it's their prerogative.
P.S. any personal items or cruicial tools you own should be removed by you starting ASAP so if it gets messy, you get out quickly with all you brought in.