yes i have made exactly what your thinking....
mine used an old (realy old) lawnmotor engine, it was 170cc, 2 stroke, don't remember the brand, but it went well, and it was the right price (free)
initialy i did put it on my wooden billykart, but that was the epiphtamy of dodgy, used the axels of a second lawnmower and wheels, i simply bolted a large pulley wheel to one rear wheel and attached a smaller pulley to motor, was about a 5:1 ratio, was overgeared, but once it was going it would have done 40-60 km/h, but it was one scary thing to drive, you steered with your feet, throttle was a piece of string, and engine brakes only... and of course the whole thing was only lawnmower width so i came close to rolling it a few times.
then i found a gem. an old kart frame (not a racing one or anything, think off road kart with no suspension, picked it up for 30 bucks, came with an old 3 speed postie bike gearbox, so the old lawnmotor engine went into that, much nicer, still one wheel drive though, went very well, topped out at about 60.
and it was rather good, i even had permission from my school principle to bring it in school grounds for some day thing we had, (my primary school principle was awesome, he was the one who initialy gave me the motor)
seeing my 6th grade teacher gunning it on the wet grass was funny as hell since she would have weighed about 110kg.
then i was caught by cops, driving it on the road (only to get to a dirt area i usualy drive it, only 200m from my house and in a very quiet street)
and was forced to sell it.
if i was going to make a kart from scratch i would definatly do some thinking to what performance you want, unless you have some good hook ups then your going to spend a bit, and unless your making somthing realy nice (which i presume your not since your using a mower engine) its probably not worth more than 200 odd dollars. in total on my kart(s) i spent about 100 bucks.
about 60 for the pulleys and belt, 30 for the new chassis and gearbox around 10 bucks for odds and ends. i also know a few usefull people in the steel industry/fabrication and know how to weld (good enough for a kart anyway.)