I'm making a universal treadle base out of a parlor cabinet, but I'm using the cabinet (had to put the treadle back in as it came missing it).
I don't see any reason you can't do what you want to, just need a sturdy base and have the sides and top fit into each other so it stays stable. Need a cross support on the back, but you can use wing nuts to secure it in place.
hmmm- that reminds me, I took all the hardware out of the small parlor cabinet I left at my son's house, a knockdown mobile treadle base is a really good idea. Now I have to remember where I put those pieces. I'm putting a lot of my treadles into bases that will easily drop into the parlor cabinet, so I could make a mobile unit to accept the same base size, and then I could use both.
Love getting new ideas!