Yes- The offload scanning server saves checksums of the files that it scans.
The fingerprint gets created when a MOVE AV Agent requests a file. The file is sent over to the oflload scanning server to be scanned. Once the offload scanning servier scans the file the file's checksum value is stored. The screen shot below is from Offoad scanning server's cache list.
Is that cache size limited or does it just keep growing and growing?
The MOVE cache size is set by policy from the ePO Server, it is limited.
For MOVE AntiVirus 2.6 'Offload Scan Server' the default 'Maximum Cache Items' is : 1,000,000 (one million items)