The Known Bugs List that I maintain on behalf of the FileMaker community stays in my drop box account at all times to that I can update it from multiple computers.
Drop Box, on windows machines, is just another folder on the computer that is automatically synched to a server by the drop box software. So I would not anticipate any major issues using it as long as you are the only user and are careful to close the file on computer A before opening the file on computer B (Otherwise, Drop box generates a "conflicted copy" of your file.)
But it is not clear to me what you mean by "the database path stops at "file:/Macintosh" "? One difference that you can encounter is that the file path to your drop box folder may not be the same on every computer. The name of your hard drive volume may differ on each Mac. This can affect the file's ability to use file paths to link to other files not referenced via "relative paths".