But isn't a Honda Fit a hatchback?
With the Accord, it depends on the depth of opening of the trunk. I have a Honda Civic and a cabinet will NOT fit in the trunk. It is amazing what I can get in the back seat, though, with the front seats pushed all the way forward. I've hauled several cabinets with drawers on one side in it...but no treadles. Is yours a two-seater or 4-door sedan? I do think the Accord's trunk might be deeper but it might depend on the year of manufacture.
I have a Singer treadle with 4 drawers in a cabinet and the top is about 17" wide by 34" long. Take a piece of cardboard (or something) and cut it to about that measurement and see if it looks like that would fit into the opening of your trunk angling it in like it would be the cabinet...that will at least give you an idea.
I think you can haul it with enough determination. Like Rodney said, take the machine out first. Take a couple of blankets to wrap things in and a couple of flathead screwdrivers--one with about 1/4" blade and a bigger and longer one. If it looks like the cabinet won't go in whole, then take the top of the cabinet off of the treadle irons, which should be attached with just large screws (which is what the bigger screwdriver with longer handle is for)...someone correct me if I'm wrong. Take a flashlight so you can see up inside the cabinet if necessary. A bottle of liquid wrench or kroil or something like that is also a good idea in case the set screws on the hinges are hard to loosen.
If you're unsure about dis-assembly, take pictures during the process so you know where everything goes. Take a couple of plastic baggies to put parts in (and accessories if the machine includes them).
I would put the wooden cabinet wrapped in a blanket on the back seat and the irons and machine in the trunk (also wrapped).
Capturing the prey is the most fun part.
Good luck.