I wouldn't go into it "blind" (i.e. without completing at least one close to full distance training run). One really needs to put in the "big" miles in order to know with any kind of certainty that one could complete a full marathon, especially with your knee problem.
By big miles, I mean a lot of 20+ milers and it's difficult to do very many long runs in the time you have left without over training. Since you aren't looking for speed you could drop any/all speed work and just focus on getting a couple/few long runs in per week in the time you have remaining. You are threading a needle between getting enough miles in and not aggravating your knee in training.
One would think that one could just slow down and run a lot longer but that doesn't work for me; essentially you are still running at a pace at which you haven't trained and for a lot longer time than are used to.
I had run quite a few 1/2s prior to my first full and thought it would be easy to ease off the pace and do a full: wrong. I remember thinking even if I way more than doubled my ½ time I'd still come in somewhere just over 3.5 hours; reality was at 24 miles I started thinking I might not finish and made it just under 4 hours (3:52).
It sounds like, barring knee problems at the longer distance, you are within striking distance. It comes down to how well you want to do and how painful you want to make it: go for a "finish at all costs" this year or put in the miles and have fun next year.