From what I understand, the problem with scaling the Moderna/Pfizer vaccines is that they use a novel process that hasn't been used for producing a vaccine at scale previously. They're having to build out entirely new factories and supply chains. This sort of work normally takes years.

Would throwing more money at the problem ease some bottlenecks in increasing production? maybe? Would it cut months off the time to complete the roll out? Plausibly. However, I don't think it'd make a huge difference to the speed of the roll out over the next six months or so. Some things just take time to ramp up.