Would it be possible to move to a new record in the ms-access database and have map in manifold GIS follow?
Yes. The way I do this now is to select the record and then zoom to selection in the map, which is a built-in choice in the drawing tab's context menu. That assumes the drawing you are using is built on a table that incorporates the access data in some dynamic fashion, which it seems would be the way to do this anyway.
I've submitted many suggestions in the past, which I know have found happy places on the "to do" list for small things that are steadily bubbling up in priority to "done" status, for increased "select back" from all panes and windows to all other panes and windows. For example, if you see something in the Record pane or in a table it should be one click to see that in an associated window (today, it's window to pane, but it should be window to table, table to window, pane to window, etc, in all combinations).