As long as the drive is mapped using the login that the SQL Server engine runs under then yes you can. So you either need to log onto the database server as the user SQL server runs under, or alternatively a handy way to make sure the mapping is under the correct user is to have SQL server execute the mapping statement:
Declare @xptext nvarchar(256)
Set @xptext = 'net use L: \\Server\Share'
Exec xp_cmdshell @xptext
Backup Log DBName To Disk = 'L:\testing_log.bck'