Probably an easy answer, but after skimming the options I didn't see an option to get push notifications whenever I recieve a PM while offline. Is it possible to have such an option turned on or does it not exist? I'm on Android BTW.

Forgive me for my ignorance!  

does not exist

but you also cannot get pms while offline(excspt via friends and search and such), which makes it pointless to have push notifications in the first place  

Thanks for the quick response, pal. Tis be a shame, but it is what it is.  

There used to be a functional thing for apple version of the app anyways where you got a notification when receiving an offline Pm. It still exists just doesn't work at least on my kindle fire. Yes there is an option to receive offline pms, this option allows anyone to pm you while offline and you get it when you log on (or whoever you have allowed to pm you).