With the caveat that I no longer own a Tiger and that my Tiger was not exactly the same as yours, yes.
The "Battery Disconnect" switch, the thing with the red tag under the sink, is a bit of a misnomer. It is a load disconnect, not a battery disconnect. (There is probably a real battery disconnect under the coach or near the batteries, right next to the main fuse. Do not disconnect this.)
Turning off the red switch should disconnect your loads - lights, pumps, refrigerator, etc., but should not disconnect the solar controller or the shore power charger from the battery. BFL13 is exactly correct. If the solar controller shuts off, then disconnect all of the loads individually.
With 200w you will see a bit over 10A with good sun and, of course, less on cloudy days. 10A isn't much, and so even with a poor quality controller, you would not run much risk of hurting sealed AGM batteries. Certainly your AGM camper batteries will be MUCH happier connected to a charge source than they would be disconnected.
So I agree with all of those who have posted telling you to leave things alone.
Depending on when your Tiger was built, you may have a Blue Sea Automatic Charge Relay between the camper batteries and the starter batteries. If you do, leave it in the automatic position and your starter batteries will be charged as well - up to the limits of the sun in the PNW.
I am assuming that you will NOT have access to shore power while in storage. I am guessing that you have the old Progressive Dynamics "converter" and I do NOT know if those are safe over extending periods of time. The Magnum inverter/charger is.
All of the above to the best of my knowledge and memory. If in any doubt, give Jay a call.
