MGOOF : Modern groupset on old frame

If I’ve got a bottom bracket installed, will it be compatible with any groupset I put on it?

It will not be compatible with every groupset, you need to match your crankset and bottom bracket. Most likely there is a square taper bottom bracket in there? This will not be compatible with a modern Tiagra group.

If you buy a modern Tiagra group, it will likely be accompanied by a bottom bracket. Most likely a 'BSA'/English threaded one, and then you only need to make sure your frame has the same thread (which most likely your Concorde will have). Either measure your bottom bracket shell width (should be 68mm instead of 73mm Italian thread), or unscrew your current bottom bracket and see which way it unscrews:

Cup direction for non-drive (left side of bike) and drive side (right side of bike) are shown below for the common ISO/English bottom brackets.

Left picture: Non-drive (left side) cup direction. Right picture: Drive side (right side) cup direction.

Italian threaded bottom brackets (shells) have the threads reversed on the drive side.