You could certainly save the access database file to Igloo but I don't know if your end users would be able to reach it from the Access interface. I would certainly encourage you to try (and I would love to hear the results).
Here is information about our desktop tool: https://support.igloosoftware.com/desktop. It is free but you do need to reach out to our support team (email@example.com) to have your site enabled for it.
Hope this helps