Look to the East
My own timeline took this premise (if in a rather tongue in cheek fashion). The biggest problem is that the Russians have to be decisively knocked out of the picture for such a union to happen- oh and also add France - and Austria - and the Baltic States - and Great Britain! So no - it's not really plausible, but it would be rather cool for such an awesome time line to happen
The Polish ruling classes seemed to be quite close to the King and Queen of Prussia, Poniatovsky seemingly got on with Louise as did other leading Polish luminaries. The problem is that the poles want independent rule, not Union with anyone else.
Russia will not condone such an alliance as they will lose their wealthy western provinces, any war between Prussia and Russia might even lose Lithuanian lands to Prussia .
Austria would fear for Galicia and maybe even Moravia possibly even Bohemia and or Ukrainian lands (Lemberg/Lvov)
The Baltic states would fear a Prussia with a reason to have a navy, and a strong one at that.
I managed it, just, but it butterflied in so many problems, I had to give up the story or start writing how all the affected nations would have to react. It did give rise to an awesome Prussian army though, complete with Polish Noble Guard cavalry!