I think that's a possibility. Or it might just stabilize. It would be easy enough to increase population again if it got too small. Perhaps after reaching a peak, it will come down to a population similar to today or less, and then stabilize?
So, if they let it dwindle to nothing, then it is through voluntary choice not to do anything about it, or indeed perhaps, even to accelerate it. There actually is a Voluntary Human Extinction Movement (VHEMT) that has this as its aim, to decrease our population to nothing through stopping reproduction.
If it was a voluntary decision, then as the population dwindled, at some point I wonder if the last few humans left might look around and say "we aren't a nuisance to the world any more, let's keep going for a bit longer?"
But if everyone wanted to go extinct voluntarily, for whatever reason - then as a unified culture of intelligent beings - they could do it. I don't think you could use evolution arguments to rule this out. Most you could say, seems to me, is to say it seems unlikely.
By the way, any extra terrestrial, or ourselves, has to stop exponential growth at some point within at most a few thousand years. After less than 7,000 years, doubling only once every century, we'd need to convert the entire mass of the sun into human beings every century to keep going. It doesn't take many more millennia to run out of matter throughout the observable universe.
So, leveling off at least, if not necessarily dwindling, is inevitable.