There are a huge number of threads on here discussing this very topic.
No you will not get an automatic upgrade to PE if BP is full for some pretty obvious reasons.
If the RU has not cleared at check-in you can ask staff who could probably give your a fairly good idea if it will or won't clear and if it's not looking good they could clear you into PE if there is space and you're happy with that.
It makes zero difference trying to upgrade from PE to BP vs a seat only fare to BP.