Yes, you just set up syncing in the normal fashion. Everyone shares the same database (and all of it, not just a subset). OmniFocus doesn't have any way to tell if it is the same person using it, once everything has been configured.
OF 1.x isn't built to be groupware, so you're on thin ice trying to use it as such. Two users editing the same project simultaneously will probably encounter problems, as the sync code just keeps the most recent change, and it is done on a per-action basis. If you change the due date and your assistant changes the note, when those two changes get synced together, one of them will be lost.
You don't have to do the sync by networking, you could also use the disk sync option, so long as you're willing to move it back and forth often enough.
Remember that two different users of OmniFocus (on the desktop) should have two separate licenses, even though the program will allow you to get by with just one.