I'm convinced it's possible in the current game at least, and I very nearly did. I spawned in an unfortunate spot of the galaxy so my empire ended up being pretty small, to the point that my home system trade hubs were able to collect trade from almost everywhere, meaning I almost didn't even need patrols for pirates. If I invested a little more in hangar stations, I wouldn't have needed the patrol corvettes at all.
Defensive border stations can easily stand up to AI empire fleets up until the mid game at least and really don't even need defense platforms at that point. I was able to keep my border stations above the largest fleets of my neighbors just by upgrading them to the biggest sizes available and making sure they had gun modules in every slot. If you have a particularly aggressive (or advanced start) neighbor, you might need defense platforms.
The real snag here is what happens if an awakened empire is near you. If you seriously invest in border stations you can beat their fleets, but it takes that investment, including a strategic coordination center and as many repeatable techs and defense platforms as you can fit on a station. I got one to almost 200K fleet power once doing this. The real problem with awakened empires is that they have jump drives, and while I've yet to see one actually bypass my border stations, I'm sure it happens.
And, of course, playing purely defensively won't work against the crises unless you're on a low crisis strength setting and are lucky enough for the galaxy to get its act together. I've yet to see the AI empires pose a credible threat to even weak crises, but maybe they can on 1x.