Although things have gotten terribly radical and sorta non-standard in the racing world for awhile, the average real racing bike of the last 40-50 years is probably too fragile.
Most are minimal tubing and either brazed or glued at the joints which are often then beefed up by lugwork. When I was racing a long time ago, it wasn't unknown for frames to break , without a motor otherwise.
On the other hand, I think more conventional heavier 10-speed road bikes may make good candidates to motor. You may have seen one that I built up over the summer and just took delivery on a kit yesterday-
The frames on consumer grade 10 speeds may be just as strong as cruisers if not more so, and for example an older Schwinn Varsity would be a good example, with standard frame tubing. The 27" inch wheels roll much better than any 26" wheel, and with alloy rims are considerably lighter, for street riding.
I can't ride the drop bars anymore anyway and I've put BMX bars on mine. With brake handles, thay are light and work well. Yes there may be a problem with bottom bracket axle clearance. Sick bikes sells some wider spindle axles for about $8 dollars and that's all you really have to change for 2 stroke.
Here's the bike you may have seen: a Schwinn World Traveller I bought from a junk man for $5 and rebuilt. The frame is lugged, but the tubing is a little bit heavier than an actual racing bike. These were made in the late 70's or early 80's I think. I'm putting a slant 48 on, to keep the weight and noise down, and because I am a little bit concerned about the strength. (I could switch later, but my cruiser already goes faster than I want to.) The new kit does not have an intake and looks like the newer carb that's just out- at least it has the white shutoff valve like it- so I think it will run pretty good. I've replaced the original steel rims with alloy- and that has dropped the weight to not much more than a racing 10 speed of that era..
I've got a chrome tank for it and an extended chrome muffler which looks great and should be extra quiet. The front derailleur will come off, and I haven't decided about the back one yet. I may usea single freewheel. The brake levers will again be combined into a dual lever which works great, and the center pull Dia Comps are excellent strong brakes. I havean extra-light 34 sprocket and so i'm hoping the final weight before fuel will be about 37 lbs.