No, sadly not. Best would be a backup of the original db rather than individual files. But that's probably not available and can't be obtained.
If the version you're attaching to is the same as the original db's version, you could try this:
Attach the db, allowing SQL to recover it (since you can't prevent it). Be sure to use the same name as the original db.
Backup the db. Drop the db. Restore the db from the new backup with "NORECOVERY". Then, still using NORECOVERY, try applying the differential and/or log file(s).
When you've applied all the files, do a final:
RESTORE DATABASE <db_name> WITH RECOVERY
If the version you're attaching to is the same as the original db's version, you could try this:
Attach the db, allowing SQL to recover it (since you can't prevent it). Be sure to use the same name as the original db.
Backup the db. Drop the db. Restore the db from the new backup with "NORECOVERY". Then, still using NORECOVERY, try applying the differential and/or log file(s).
When you've applied all the files, do a final:
RESTORE DATABASE <db_name> WITH RECOVERY
to make the db operational.