Yes, if you tug at the roof connector, the whole assembly will come down. It is designed to detach relatively easily in case your head hits it in an accident. It can be a bit tricky to put back, though, but nothing that a bit of perseverance won't solve!
There will be some wiring running from the roof to your mirror (because yours is photochromatic). Watch you don't pull too hard and pull the wiring out. There is probably a plug connector that will enable you to take the mirror away from the wires.
I know that a new photochromatic mirror without a wiring loom is 125 GB Pounds. That is about $150. Good luck.
1999 SL 500
1993 320 TE
1986 500 SEC