I would suppose it should. but would be worried about the tires wearing out. About your little gizmo, I disagree with tony. That looks like 3/8 plate. It will NOT bend, but... I don't know why you are using aluminum. Steel is the way to go for anything structural. Not sure how you can attach it to the frame as it cant be welded because its not steel. I would use steel instead, as its not brittle at failure, can be welded, and has a much higher modulus. Steel is 3x stronger than aluminum given the same scenario. 30gpa vs 10gpa. Like Lewiebike i would have the engine above the wheel and not in the frame.
Here is some stuff. You didn't give dimensions. I assumed you have a 3/8 x 4" x 8" plate of aluminum. If your plate is less than 3/8" i would fail it. Even 1/2 of that, around 3/16 would mean 8x the center deflection. So you take 0.03x8 and get a whole 1/4". That's horrendous. 3/8 is the bare minimum. To bend this out of standard deflection tolerances.... Assuming its placed flat between two points like plywood such that its only 3/8" tall and 4" wide and spans 8". Here is the graphs of the forces. I know you have it vertical and with gears and crap so its not a purely accurate representation but....
The moment of inertia is 0.0175