Vote in poll

No, there are too many options to keep your inbox clear. You can easily delete, or archive your messages, and you can increase the size of your PM box if needed by purchasing FG, and make it even larger by getting verified. More info here.
It would be counterintuitive to become verified and increase the size of your PM box, if other users could simply pay some FG to bypass your box being full. Since this is a new system, I don't see your suggestion happening.

voted no

i know its very annoying if you want to pm some1 and his inbox is full, but i think paying fg to increase someones pm box is not the right way since everybody should only pay himself for benefits of the own account. Furthermore imo the effort to implent this feature is not in proportion to its use, sorry.