Folding bicycles are frequently purchased for use on public transportation. Unicycles are much less commonly seen, but train conductors would probably treat them similarly, especially because they both have rubber tires that may be grimy/wet/dripping. Folding baby carriages are another possible analogue (though that case explicitely involves two different riders, sometimes with two paid fares).
(traditional bicycles can't be taken on Metra during rush hour, and there's a limit of 5 bikes per traincar)
(traditional bicycles can't be taken on the train from 7-9am and 4-6pm)
Portland's TriMet: Folding bikes must have wheels that are 20" or smaller.
"I think one key to taking a folding bike onto no-bikes-allowed public transportation is what the folded bike looks like. The less it looks like a bike, the less trouble you’ll get." (...so bring a duffel bag that can cover the whole unicycle, turning it into an oddly-shapped duffel bag and nothing more)
I've gotten word from the Portland unicycle community that TriMet is apparently cracking down on allowing folks to take their one-wheeled rides onto buses with them. ... "Thank you for the opportunity to clarify TriMet's policy on unicycles. ... unless they were a 'folding' unicycle as set forth in our rules, they would not be allowed on buses." (TriMet defines a folding bike as one with a collapsing frame that has ≤ 20" wheels)