You have a security tag to open doors with?

It it was a random small business maybe, but a real datacenter? Not a fucking chance, the company needs to request entrace with names, ids and request any hardware that will leave or enter the place (model, serial number, etc)
You probably watch to many movies.

0% chance.
You have to be on the guest list to get in to those places. They don't do the "oh I'm here to see Jeff" thing.

If by some miracle you managed to fool the security guards, break into one of the data halls, and actually leave with hardware, you would have the FBI after you. The only people willing to go to such lengths to steal hard drives are corporate spies or foreign intelligence agencies.

Not very. Although I will 100% tell you that small operation crypto-farms are easy game. Half of them don't even know how to do their own tech.