I have heard that the Boeing Plant in Everett, Washington is so large that a Cessna could fly around inside it no problems.?

Yes, it is the worlds largest building in volume and would certainly be big enough to fly a C152 inside it for a short distance if it was empty.

It has been quite a few years since I was there, but I don't recall any major structural obstructions, although the roof is only about 200 feet high from memory.

I do recall that each doorway is the size of a football field, so long as you did not go too high you should be fine :-)

Certainly, if there were no aircraft along a final assembly line there is plenty of room to get airborne and fly out through one of the doors.

No problems? False. It could be done, but barely.