Would it count as a PS4 playthrough if I used PS4 remote play to play it on my PC so that I could record it?

Yes. The PS4 is still what's running the game, remote play is essentially just another option for display output.

That said, I'd expect remote play to have some pretty nasty latency so that may not be the best option for speedrunning.

Thanks! I know there'll probably be latency but I don't have a capture card or money so.

My man, forget about the remote play. You can just record or stream from the console.