So, can you do a triple dipping?
You first upload your song to a distributor like DistroKid, then you upload the same WAV to a sync library like Songtradr, and finally you upload that WAV to a PRO like ASCAP.
In this case, you can collect royalties from three separate sources.
Are you allowed to do that? Is there gonna be a copyright conflict between a regular publisher and a sync library?
No. You don't triple or double dip.
Your pro only collects income. They don't distribute or publish. You can upload a song but it's only for registration. Your publisher should do that on your behalf and if you are in a non exclusive library you can have one song with multiple registrations but each is tagged uniquely to a given publisher. Whoever is responsible for publishing a song in a specific place is responsible for the royalty to the pro.
Streaming services pay for streams on their platforms.
So no. You're only getting paid from the one publishing company that got the song in the cut. You can have one song producing multiple revenue streams but none of those are stacked.
I hope I explained that clearly enough.