Gearing up is not necessarily going to get you faster rapids, mostly because at some point you won't have enough torque at the screws to accelerate. If you could provide more info on your machine/motors, that would be helpful.
Another question is, why do you want such high rapids? And do you do a lot of rapid moves in normal usage? By gearing up, you are likely going to be reducing overall torque, which means your max cutting speeds are likely going to go down. Another question is, what is your current acceleration? If your acceleration is not high enough, then you will not hit your max rapid speed on short movements, so you would not get anything out of the deal in most cases. The only way you are going to be able to see if you are going to get any improvements is to try it, or find the torque curves for the motors, and see what they would be capable of at the new speed/torque
Now, if you already have a belt drive system, then it would be pretty simple to swap out pulleys and a new belt, and re-configure mach to see if this will help you, and you can always go back. Pulleys can be pricey though...
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To add, yes, you will lose some accuracy doing this (accuracy will be reduced by the amount you gear up, unless you have linear scales... in which case ignore my last comment, nothing will change). The question is, will that loss in accuracy matter. At 200 steps X 5 tpi, you are getting 1000steps per inch (0.001" per step). Not bad. Likely you are also using some sort of micro stepping, so assuming 10x micro stepping, that brings you to 10000 steps per inch (0.0001" per step). Do you need that? Probably not. Are the mechanics of the machine even capable of that repeatability and accuracy? Really unlikely. Another thing to think of is that with a simple parallel port setup, you will likely not be able to generate steps fast enough to reach those speeds, you would need something like a smoothstepper to get there (which, maybe you already have).