I do not believe Access has robust history like SQL Express does. You maybe could create something with SQL triggers.
As you probably know you cannot submit to a seperate table from Infopath with out Web services. With web services it would be pretty easy to keep a audit table up when it was submitted.
Another option is adding the User and Date stamp to your main data table and updating it on submit but this would be somewhat limited and would make your reporting more difficult but would be doable with your current architecture.
This is a typical issue that comes up with the InfoPath database form + Access architecture.
I think you would have to do something on the SQL backend with triggers to monitor table changes and create the audit but I do not think that Access has anything out of the box to do this like SQL does.
Maybe someone else will have another idea.