Yes, I believe it has a big influence. Most propellers are chosen based on numerous variables and the most efficient propeller is normally anywhere from 2 to 4 blades. Power, rpm, pitch, air density, maximum noise, maximum diameter, intent are all relevant? If you want greatest power efficiency, this is likely different pitch than maximum thrust, and noise tolerance may make a big difference. In flying an ultralight, I have seen mostly 3 bladed propellers, but if you search "flying car and missionary," you will see that the 2 or 3 person Maverick uses a fairly large (car sized) power plant and a large diameter 6 bladed prop. I can guarantee a lot of thought went into the choice of this custom propeller. Just like a wind turbine, if the prop turns fast and has too many blades, the draft left by the previous blade can cause inefficiency or possibly stalling or "pulsations."
For thrust needed at 3 feet - if you are trying to suspend a 400 pound load including power plant and pilot, you will want that much thrust. However, at only 3 feet, the ground effect will likely reduce this significantly.