Well, sometimes... sometimes not... sometimes kinda...
For instance. Chaintech VNF3-250 and 90nm Semprons... not officially supported except in latest BIOS but worked fine with older BIOSes even though it boots saying something about unknown CPU. I've seen boards that did have some oddities like always having to hit F1 to when machine POSTs because "invalid microcode" (seen that in some Asus boards such as P4S8X-MX and mobile CPUs). There are also some that may not POST at all - can't think of specific examples but I'm sure they are out there.
One thing is that if the CPU is of a similar family that works in the board, then there's a good chance it will work. For instance, if the board supported Venice core up to 3500+ and latest BIOS adds 3800+ support, the board will likely work fine with 3800+ on the older BIOS. Your choice of San Diego... I think 3700+ is slowest one so that's a tough one. Well, I think there's a good chance it can work if the board supports Venice.