Can a lost Apple Pencil randomly reconnect if it’s just lying nearby?

Based on what you described, no, an Apple Pencil (particularly the 2nd generation, which I’m assuming you have since you mentioned it connected automatically) won’t just randomly reconnect if it's simply sitting nearby unused. For that brief connection to occur and show 1% battery, it had to have been physically close enough and magnetically docked to your iPad — even if just for a second. That only happens when it's placed on the edge of the iPad where it normally charges and pairs.

So the fact that it popped up on your screen almost certainly means someone either had it in their possession nearby and momentarily attached it to your iPad without realizing it, or it might’ve been sitting somewhere really close (like a desk or shelf you leaned your iPad on), and just happened to get close enough to register. But again, these pencils don’t just “connect” out of nowhere like AirPods might — they need that magnetic physical contact for that brief sync moment.