With the Beatles' five man line-up, including Stu, what exactly was Paul's role? Second rhythm guitarist or second lead guitarist? Every indication seems to be that he was a rhythm guitarist. Did he occasionally play lead?
More to the point of your question, might Paul have played bass notes on his guitar to cover up for Stu? It's certainly not unheard of for a guitarist to double up on what the bassist is playing (or in Stu's case, supposed to be playing). The Beatles certainly did that on "Day Tripper", with guitar and bass playing the main riff.
If Paul dreaded the thought of being the full time bassist, he certainly did jump into the role quickly and competently, didn't he? While his best playing started after the "Help" album, he was no slouch on their earlier work, given what was expected of a rock bassist in the early 60's.
So why do I think that Paul, even without a bass guitar, was more than prepared when the time came? Even if it was just out of boredom, I can see where Paul noodled around with bass lines before he ever touched a bass.