It will work, providing the database contains no persistent enterprise-only features (partitioning, compression, TDE). If the DB uses any of those, the restore will fail *at the end*
Backup compression isn't a problem, while only Enterprise/Developer edition can create compressed backups, any edition can read compressed backups and restore the DB.
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability