Yes, definitely yes, I'll mark this for you, I have a 66cc, on a standard sick bike parts jackshaft kit, sprocket size wise that is
I weigh 210 pounds, bike weighs roughly 40, and I have a bicycle trailer that is rated for 100 pounds of children meat, I try not to exceed that with groceries, but have in the past. Add my 10 pound bag of tools in my big ass milk crate (sexy and you know it)
Now I like to shop the wally world (Walmart for the norm folks) up the main road from me, on the way home. At least 3 Hills at a 20degree incline, and one nice 35er, about 4 blocks long a piece.
Math magic gives us a whopping 360 pounds to be taken 3 miles from the alien mart to home base, up some rather nasty hills. Never experienced a problem while towing, thank God, only have problems when I'm not bringing home ice cream in the middle of summer.
I've pulled it off in rain, and once with maybe 25 pounds of stuff during a light snow.
Yes, bikes can, and will tow, shift kit recommend as you can take it slow in a low gear and work your way up on flats. And no, with a shift kit I've never had to assist any tow job up a hill, in fact I mostly can't assist it, anything above idle speeds and the chainrings move faster than I can physically pedal to overcome the freewheel mechanism.