It physically fits but isn't very stable. The Chemex's glass is also a bit thin so I might hesitate pushing down hard on it since might put stress on it. I'd probably brew into a mug and dump the coffee into the Chemex if you want to serve it in that.

I like brewing Aeropress into a frothing pitcher. Super sturdy, always the exact right size, and the spout makes it easy to cleanly pour into other vessels (I make iced coffee in pint glasses often).

You could use a metal french press instead?

Not directly answering your question, but the metal v60 server works great on most devices, and keeps it warm https://global.hario.com/product/coffee/server/VHSN.html