This is indeed possible, depending on what version of SQL Data Compare you have. I believe this should be supported with version 6 and later (currently on 8) and if you have the PRO version of the tool.
The syntax (with version 8) for using a backup as the source and a DB as the target, and then performing a complete synch would look something like:
sqldatacompare /b1:"FULL_SQL2008_AdventureWorks2008_20100414_000000.sqb" /s2:"pete\sql2008" /db2:"AdventureWorks2008" /synch
If however you download a trial from the Red Gate site, open up CMD and run sqldatacompare /? /verbose this should then output a full list of switches to the console for you. With regards to the automation, once you have saved these commands as a batch file you can then set the file up to run with Task Scheduler.
*disclaimer: I work in the Support team at Red Gate