Good idea, but I think there are better choices for a frame, honestly. And.... no, I don't think they would envy you with an HT on that thing. Maybe an electric motor, but anyway...
I was actually just looking at a few of these tiny bikes on eBay 2 or 3 days ago. Here are some good ones....
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Just Go Runt" bike, which is almost identical to the bike you got... but is a poor choice for motorized applications, IMHO.
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Origin Mini BMX, which has some fat wheels, which would make for a fairly smooth ride.
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Then a random bike with 12" (?? 10"?) wheels, gets pretty low rolling resist
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And another
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And another
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And you get the idea by now, right?
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The CarryMe DS would be great if you have super flat roads (DS stands for "dual speed", which comes from the Schlumpf drive; you can save a few hundred and get the single speed, but that's no fun.
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The CarryMe DC was a CarryMe single speed that was pre-built with electric motor functionality, but it appears this retailer doesn't sell it anymore. You could probly build one for several hundred cheaper than they wanted anyway!
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And there's alway the drill-powered bike for inspiration; but I'd rather put that on something with AT LEAST 10" wheels.
I love small bikes, but 10" wheels is the limit. The CarryMe bikes are the only exception to that rule because that bike has other selling points, like it's geared properly out of the box and folds into a very narrow form. Other than that, tho.... I'd imagine 12" to 14" wheels are the hotspot.
I found a couple folding bikes with 14" wheels, but the gearing was way too low. But I turned one of 'em into a fixed gear folder and cranked up the gearing from like 30 gear inches to 60". The average BMX is geared at around 55 gear inches. If you can ever get a small wheeled bike in the mid 50 gear inch range, you'll have a blast. I'm thinking about maybe putting an electric motor on the 2nd one I've got, but the only way I'd want to do it is with brushless hub motors, and these 14" rims are fairly hard to find [if not impossible], so I don't want to tear a good wheel down for nothin'.