No. Deleted log file breaks the log chain (among the nasty things if can do), so you need a full or diff backup (probably full) applied to the secondary to restart log shipping.
Don't delete the log. It's not an optional file.
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