Should I include over-voltage protection for a 3.63V max device using a Lithium-SOCl2 3.65V battery?
I'd suggest you DO need some form of regulation.

Looking at the datasheets for the batteries, the nominal voltage is 3.6V BUT it is temperature dependent. 
This datasheet from Minamoto shows the terminal voltage rising to about +3.8V at 70&deg;C.



If you can guarantee that everything on your board will tolerate 3.5V, then you could use a low dropout linear regulator such as this Ablic LDO. This has only 53mV dropout voltage and should follow the battery down below that point. It's available up to 3.5V.