Just in case anyone else didn't figure this out, found out how to get Dropbox to start up with an antiX session:

Go to antiX Control Center > Session > User Desktop-Session
When the editor opens, pick the startup file (as you should), and add this:
I had to track that one down by looking at the contents of /usr/bin/share/applications/dropbox.desktop
For whatever reason, the dropbox command in the CLI shows neither of those options with $ dropbox --help

Anyway, hope someone out there finds that helpful.