If the player is doing it in an obviously calculated way (eg standing in an offside position trying to block the GKs line of vision at numerous free kicks) then yes.
Can see that this could also be construed as UB. But I don't see anything in the Laws that preclude (deliberate, irritating!) offside offences from being included in the definition of PI?It would be USB, not Persistent Infringement, you're not sanctioning the fact that he's offside, you're sanctioning the fact that he adopts an unsporting behaviour
No it's a technical offence, a bit like persistently taking a throw-in incorrectly, which you wouldn't caution for eitherAre there any circumstances when you might caution a player for being persistently penalised for being in an offside position?