As I understand it, the baby stay adds a measure of stiffness to the mast, and pulls the mast forward from its attachment point, usually against the tension provided by the aft running check stays.
All together, this stiffens the relatively 'bendy' masts of the later C&Cs and prevents (or minimizes) any fore and aft mast pumping in a seaway with swells, etc. Such pumping could lead to a mast that is bowed aft--not a good situation.
I do not go offshore with my 36 XL/kcb, which had an adjustable/removable baby stay. The baby stay was a PITA to tack going to weather as it would catch/damage the headsail and was another PITA to remove and tie to the mast so we could fly a kite. I removed it permanently as my spreaders were not angled aft but I still use the check stays that run aft to help stiffen the mast on upwind legs.
OTOH, if your mast is more like a telephone pole, it is not going to be bent by a baby stay. In that case, especially if your spreaders are not angled aft, it may not be very useful.
I did save the baby stay hardware just in case I venture offshore--in which case I would probably reinstall it. My mast is pretty bendy and in a seaway I would feel better if I could control the bend as I stiffened the mast..
FWIW,
Charlie Nelson
Water Phantom
1995 C&C 36 XL/kcb