No, at least not what actually disappeared.
What if China and its silk was still there? What if just the land in the middle disappeared and China, Mongolia and half Russia was still there? Big difference in size and economic perspectives.
And they have at least a vague idea of its size and location.
If we were talking about knowing that some land disappeared I'd say sure, like many others have. It could be religion when it tries to explain what happened. It could be someone who knows and explains to the farmers why the climate has changed. Or it could travel through gossip and merchants, it's a huge news that will be shortly confirmed by the climate after all.
But while we know that the whole thing disappeared, they'd have no way of knowing it. Maybe everything disappeared but China, making it an island. If it were any other state with lower trading importance they may just assume that it was gone, but in this case people would probably still have hope that maybe only the land in between was gone. And if Europe was still there, maybe also the other side of the continent was still there too.
But they couldn't just go there blindly hoping to find something. 752
From the nearest point to halfway through China there are roughly 4000 km. It took seven years for <PERSON> to find someone who financed his travel which was, according to his estimation, of roughly the same length (3860 km). The difference is that in that case there were estimations (even if bad) while in our case there are none. In the worse case there is no land at all (they don't know that it's actually like this) and the ship is neither able to go around the earth nor able to return back.
At most they'd be able to reach the border of current China and return back, but even there, there is a big piece of land afterwards that they'd have no way to know if existed. To see if their trading partner was fully gone they'd need to travel 12000 Km in the worst case, which is way beyond what they could do at the time (or willing to do due to the costs and danger).
It's important to notice that the potential disappearance of the whole continent would prevent both <PERSON>' voyage and the discovery of the sea route to India below Africa. This would probably prevent the Age of Discovery from happening and also inhibit the development of long transoceanic travels far away from any land.
For this reasons it'd take more than two centuries before anyone is actually able to tell the size of what is gone and even there they'd probably just check for China and assume everything else was gone too. This would allow for islands of the size of Europe to be overlooked (like the whole east Russia), but we are not interested in precise knowledge. I'd personally say much more than two centuries, but we are already far too deep into an alternative timeline for that. 989