Well, maybe, with a few caveats:
Read a book about how to sail first, and really pay attention and think about what you've read, envision doing it in real life.
Do all your sailing/learning in 5-9 knots of wind, no more, no less, steady in direction, no current and flat seas, and away from other traffic
Do this lots, like every week, if you can get those conditions consistently
Carry a vhf radio and have someone ashore who can answer sailing questions as they come up.
That might give you the absolute basics, but then you'd have to learn reefing, heavy air sailing, and Oh, I forgot--man overboard recovery. And sail shape, navigation, chart work, rules of the road.
If you can get these conditions reliably, you might learn, I've seen people do it that way and come out okay. But if you can't, or don't get good "learning" weather consistently, or don't have the time and dedication, then take at least a couple of lessons. I'd recommend Power Squadron too, but maybe you already have this.
I'm biased on this, I suppose, as I teach sailing as a part-time gig, and think it's the better way to learn, but I have seen people teach themselves to sail. You may pick up some bad habits you'll have to unlearn later, though, and please duck during those jibes, they don't call it a "boom" for nothing.