I hope I can share my experience traveling while waiting for PR. I was very apprehensive, but everything turned out just fine!
We used the European passport return so we already had our passports with us, but marriage certificate and translation were with HO, so I printed a copy of it and my husband job contract, some proof of him exercising the treaty right and the COA letter.
I traveled with my husband, and when we arrived back in the UK, I've waited for the officer to ask what was the reason for our trip to UK, I explained that we already live in London, but I was waiting for my PR result and didn't have any visa with me for that reason, he asked if I could prove it and I showed him the COA letter. He only said for me to always bring this letter with me when traveling and that was it! He didn't stamp my passport or asked any question relating to our marriage.
I suppose if I was traveling alone he would have asked a whole lot more questions.