Yes, the baby stay keeps the mast from "pumping" when you are slamming into waves. It's one of the great features of the the 361, because it makes the rig so strong. I wouldn't remove it unless you are always sailing on flat water (like an inland lake). Even then, I'll bet your insurance company wouldn't cover a dismasting if they find out you removed a stay.
The 361 is so beamy that stern davits work very well for hoisting a dingy, which is much more convenient than putting one on deck. Plus let's face it, dinghies on deck look like hell!
Happy New Year,
Agaliha
2002 B361