These bacteria aren't going to be Andromeda-strain like superbugs that can eat through plastic in seconds. Plastic that is dense and strongly crosslinked will take much longer to decompose, fortunately.
Instead of uncoated paper, what about waxed paper? It's impermeable on a reasonably long timescale, and is fully biodegradable too.
It doesn't have to happen that fast to be bad. Such bacteria would be like rust to metal. A lot of our things are based on plastics; it would not be good if suddenly everything started to "rust" and break.
Then again, some companies might like the fact that it could be another form of forced obolescence...
Personally, the inertness of plastics really suggests recycling and reusing; it's somewhat sad that we've invented materials that can last almost forever, and yet so many people are treating them as disposable and creating waste in the process.
I was thinking more along the lines of contagious plastic-eating rust destroying civilization by attrition, but yours is a scary thought as well. As for plastic waste, I just vented out about it yesterday. https://news.ycombinator.com/item?id=10308556.
Instead of uncoated paper, what about waxed paper? It's impermeable on a reasonably long timescale, and is fully biodegradable too.