You can. "PGCE with QTS" courses generally require either any degree for Primary, or a subject-relevant degree for Secondary. An OU degree is fine for this, and actually that route seems to be quite popular.
I assume you've ruled out doing an Education undergrad that does include QTS at a brick uni. That'd be the fastest option, but obviously not everyone's circumstances allow it.
You might want to consider doing your OU degree in something other than Education, so you have a backup plan if it turns out teaching isn't for you?
I can't answer your GCSE question, sorry.