1. If you have a confirmed dinner reservation, the only reason they wouldn't allow you to hop there would be in case of a "hard" capacity close...which are extremely rare. Holidays or possibly October 1st this year may be the only time you should have to worry about that.
2. I wouldn't say they'll necessarily rush you out, but you won't be allowed to meander around in the parks. They keep everyone moving toward the exits and do not allow you to wander. They'll make sure you take the shortest, quickest way out. As a matter of fact, it's probably best to hit the restroom at BoG before leaving.
ETA...I thought you meant hurry you out of the parks. No, the restaurant won't rush you at all.