I'm not sure it accrues, or at least doesn't in some circumstances.
This guy has been my starting catcher in FOBL for the past three seasons:
Player Report for #46 Raúl Medine
He had about a decade off where he was pitching (though not very well, which is why he returned to C). Lost his experience at C which is fine, but he still had some ability there. Despite playing there regularly though, he has no experience (I checked the raw value - it's 0) and thus no position rating.
Not sure if this is intended or not.