It is of course possible to test stuff in a 3D environment. Big companies for example do it when they build a factory to check whether any pipes intersect with the walls or cables. Better safe than sorry.
Doesn't mean it's easy in Blender. You can misuse Blender as a CAD-Software. I have used it to visualize stuff I wanted to build in order to find out lengths or shapes. Turns out it does a reasonably close simulation of a solar eclipse, too. You could write a script that accurately checks for intersections.
Realtime physics can help as well.
All of the simulations in Blender are not built for high precision. Especially the physics are meant to be an amazing aid to animation, not a precise model of the world.
Also, most 3D printers have tolerances which means: what you model is not precisely what you get. Gears will work, just not amazingly well. You can't beat bought gears or a solid lathe to make them yourself with a 300 bucks printer.
Quick answer: it helps and you can model the parts for the printer but you need to gather experience to foresee all the pesky little details involved.