By definition they favor government.
Technically, no, it doesn't. It means that they have governed. You can make the argument that this means that they tend to favor government, but it is not actually part of the definition.
The same logic would say that anyone who's ever held elective office is ineligible because they "favor government", which would mean handing the most powerful political office in the world to someone with absolutely no political experience or track record to judge him/her on.
I can't say that I think that's a good idea, on the whole.