Nope, won't work. Lots of variations in the T56, and the caddy version has a different tail housing that's not interchangeable with the F-body one. It also has an LS input shaft and (I believe) triple/double synchros opposed to the F-body's double/single synchros which renders it impossible to swap in an LT1 F-body input shaft.
The only T56's that will work with the LT1 besides the original are the LS1 F-body T56's, which require swapping out the input shaft and using the LT1 bell housing to work.
The only T56's that will work with the LT1 besides the original are the LS1 F-body T56's, which require swapping out the input shaft and using the LT1 bell housing to work.