The problem isn’t with open files, it’s about a big binary file that is written while it is copied. That’s why mysql is dumped and dump are synced.
BTW, you get an email when a file changes during it’s copy (other kind of alerts coming soon), you’ll know if it doesn’t fit to your scenario.
it’s that. In your case scenario, you could use it dumping access db and copying the dump. Or like @planet_jeroen suggested, setting up a real HA.