Only if you keep the phone from shutting itself off due to inactivity. And given how long afk can last, you'd better have it plugged in, too.
So far, connecting/disconnecting crashes POL when the screen flickers as you connect to the computer, so you have to start it after you connect (and log out before you disconnect). However, it may be possible to adjust your monitor resolution or tweak some settings so that doesn't happen, and you can leave FFXI running and just check in on it once in a while.
In that case, it could be pretty convenient for periodic check-ins, say for bazaar, AH, between windows to pretend you're there to help claim but really are just waiting for pop so you don't have to get off the couch until it actually pops, etc.