It looks to me by the way the ICE is solidly bolted to the frame, it contributes to the beam and torsional strength and rigidity of the frame. Without this contribution, the remaining frame structure may be stout enough to handle he forces applied to it. But, you should watch for excess flexing of the frame that might lead to cracks forming. In this case, an additional structure may need to be added to the frame to strengthen it and make it more rigid.
This is a bad idea with a motor designed to turn up to 10-12k RPM, at maximum power. I don't think there will be enough power reliably available at such a low RPM. Also, if you try stepping up the motor RPM to get more power, with this direct drive to the stock flywheel, you could run a serious risk of the flywheel coming apart.
A slow turning, large diameter DC brushed motor would be a much better fit for this kind of simple, direct drive set-up. The motor control is also much simpler. You should check the used forklift motor market.