Basically as the question asks, if you set up an alcohol vapor cloud chamber with the gold foil inside, wouldn't you be able to "see" the alpha particle's path the entire time? It just seems like the demonstration would be way cooler (pun not intended) and visually interesting. I'm just wondering if any issues would arise that would cause the two experiments to interfere.
It seems that Rutherford himself saw the tracks of alpha particles in a cloud chamber,
Cloud formed on ions due to α-Rays (Image: CTR Wilson Roy, Proceedings of the Royal Society A, Volume 85, Plate 9)
. . .
The tracks of the particles become visible as trails of droplets, which can be photographed.
I'm just wondering if any issues would arise that would cause the two experiments to interfere.
I do not think there is a problem of interference. The original experiment was in a cloud chamber after all. See a video here.