Is it a bad idea to stay plugged in with the battery out or disconnected.
On a 20xx, no problem at all. on a 1970 Perhaps. But the deciding factor is the Converter. Most modern RV's have either a Parallex 7300 or equal (Single stage) or a WFCO, IOTA or Progressive Dynamics 3-stage charger. (PD's are made in Michigan and in my not very humble opinion based upon over a decade of research you will not find a better one.. I've known about this company for years and they make truley great stuff).
Back in the old days you might get a Magnatek 6300.. and if you have one.. UPGRADE to a Progressive Dynamics 4600 line.