Of course yes.
But was the Ring aware of how much time had passed between escaping Isildur and being picked up by Deagol?
I don't think there's any way to know for sure, but I find it plausible the Ring wanted to stay at the bottom of a river that long.
As Gandalf says, "His Orcs have multiplied; his fortress of Barad-Dur is rebuilt..." So it's possible Sauron's timeline would involve taking long enough to let the heat on the Orcs and his other servants die down, for history to fall into myth and the various armies to disband and/or turn on each other, and then for his servants to have enough time to rebuild their numbers, equipment, and fortress before he returned. In the meantime, if the ring was bouncing around bearer-to-bearer odds are high somebody will find out and toss it in Mount Doom before there are any defenders or fortress to prevent that. Safer to roll around hidden in the mud at the bottom of a river for a couple of thousand years and let history take it's course.
He may even have decided to wait for Smaug to grow large and powerful as an ace in the hole. Personally, I hold the fanon that Gandalf arranged the events of
The Hobbit entirely to get Smaug out of the picture and remove what would otherwise be a mighty tool in Sauron's arsenal before Sauron was entirely returned. Finding the Ring in the process wasn't part of Gandalf's plan but there were many forces stronger and wiser than Gandalf at work in the world.