When I rode east to west starting on the Northern Tier, I saw a few people finishing their east-bound tours but didn't talk to anyone until I met a couple in Vermont. Then, every time I met cyclists, we'd almost always stopped to chat, give a few heads-ups for the route ahead, trade war stories. I camped out with an Adventure Cycling gang in the Adirondacks--huge fun. As a soloist, these meetings were real soul food. There's nothing quiet like touching base with someone who really GETS what you're going through.
My favorite encounter of this type was meeting up with a fellow with whom I'd developed a minor e-relationship. He would be getting out of the Marines and heading west to east. I was heading in the opposite direction. For the first third of my route and his last third, we'd both be on the Northern Tier. So, yeah, for sure, let's meet up. How likely is that? Different start times, rest days, off route meanders--who knows? But one morning in eastern Ohio as the mist slowly lifted off the cornfields, I saw a cyclist headed my way. We both stopped on opposite sides of the road: "Steve?" "Scott?" A classic encounter! We stood in the corn for half an hour chatting about everything from storms and mosquitoes to the Iraq conflict. It made me wish we were going in the same direction.
After that, I didn't encounter another long-distance cyclist until eastern Colorado when I was on the TA route. I met a couple of guys there. My last cyclist met was in Arizona. He was on his way to South America. We hung out for a bit as I fixed a flat.
Meeting other cyclists is one of the great pleasures of the road. Whether to stop or not should be natural enough.
Report back after your ride!