Music boxes were gaining currency in the 19th century (https://books.google.com/ngrams/graph?content=music+box&year_start=1800&year_end=2000&corpus=15&smoothing=3&share=&direct_url=t1%3B%2Cmusic%20box%3B%2Cc0).
Other artists have been inspired by production level crafts (Lichtenstein).
Chopin would have been training concurrently with the existence of music boxes.
Chopin's tempo rubato sounds like playing a corretly times music box with varying hand cranking speed.
It's a very fun idea. I see two problems. One, the rotation of the crank for barrel organ/ orgue de barbarie never seems to match the rhythm of the music, so producing the classic rubato is really hard, since for that you have to "buy" time in one spot and "give it back" in another to make the overall tempo right. It's hard enough to keep the cranking as smooth and steady as possible just to play an even tempo. Rubato's even harder. Don't take my word for it: if you can find a barrel organ/orgue de barbarie ( a fair number still exist in France, often accompanying street singers) try to get permission to give it a crank. It is surprisingly hard to play one.
The other problem is that spring-powered clock movements, not hand-cranks, would commonly drive music boxes in Chopin's time, after 1815. The crank would only wind the spring.
However, if Chopin ever admitted to being inspired by music boxes, likely somebody made a note of it at the time. Wouldn't hurt to sift through a biography of him.