That option is most likely greyed out because of a group policy set by the network administrator and it would have to be changed by the network administrator.
I use remote desktop all the time, and I can tell you that only one user can have control at a time. You would know that your computer guy is into your machine because it would lock your computer and you would have to use crtl+alt+del to unlock it. Remote desktop does not let your employer monitor your computer usage, but there are many other programs out there that can.
I use Remote Desktop all the time to fix issues on machines in another part of our building, or at our other company several hours away, and I usually give them a call and tell them that I am doing so, as not to scare them.
A work computer is usually company property, and the company has the right to restrict or even monitor your usage as they see fit. If your employer has a usage policy, it would be a good idea to adhere to that policy, I would not want to see you get into any trouble!