No, I'm pretty sure Arcserve has a exchange option. You should invest in that to fix your problem, after a succsessful online backup with this option all the log files will be flushed.
You don't need to backup the M: either by the way - it will be pretty useless to you in a restore.
For more info, here is a note taken from the Exchange Admin companion;
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Never, never, never delete your log files. Here's why: Assume that log file 9 contains a command to insert a new page at a particular place in the database. Log file 10 contains a command to delete this page. Now suppose that an administrator deletes log file 9, perhaps thinking that the file's timestamp is too old, and also deletes the checkpoint file. The administrator then needs to reboot the system for unrelated reasons. When the Store.exe process is started, ESE automatically enters recovery mode. Finding no checkpoint file, ESE has no choice but to replay all of the log files. When log file 10 is replayed, the delete command will be carried out on that page, and its contents will be destroyed. ESE won't know that there was an earlier command to insert a new page in that location in the database because log file 9 was deleted. Your database will be corrupted. Whatever you do, do not delete your log files or the checkpoint file. Furthermore, be aware that write-back caching can have the effect of deleting log files. The best practice is to disable write-back caching and never delete your log files or checkpoint file.
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