Will keeping all my fans at 100% speed harm my computer?

The only harm that would come to your computer should be the fans wearing down faster. If you have an insufficient power supply, this might harm it too, but it really probably won't (I mean, I've never heard of a PC fan drawing enough current that it pushed a PSU over the edge… but anything that has a load could present the possibility if you're already borderline I suppose). And the dirt and dust accumulation would require constant vigilance.

I do run my desktop with the fans on a constant (non-100%) speed, since even under full load it doesn't get particularly warm and I prefer a constant level of noise to a variable one. A few months ago, one started rumbling. I popped the actual fan part out of the center (it was on a sleeve bearing one; ball bearing fans often are assembled differently), cleaned it out, and oiled it, and the rumble went away again. It's not come back yet. So far I think I've had these fans for five or six years.

Really, I would just configure the fan speed in the BIOS if possible (you can on mine, but I built my computer myself. I don't know about OEM motherboards). It's more reliable than some random program on your OS that does whatever the hell it does to keep the fans up.

If you don't know how it's keeping the fans up, could just be making the CPU crunch more numbers and heating it up so the OS reacts, for all I know. It could even just be mining bitcoins for the author. So why run software from more sources than you have to and increase the number of people you have to trust?

So anyway, people who make computers and fans know what they're doing. I wouldn't mess with it, because it wouldn't provide a noticeable boost to speed (even if technically the overall speed is 1% higher or whatever).

If it's a laptop, then the same rule applies, although often the OS will provide a power setting to determine if it activates fans or instead down-clocks the CPU more or less aggressively. Windows does (or did as of 7) somewhere in the power management control panel. I believe the Linux kernel has similar sorts of functionality; I can manually set my fan speed on my thinkpad that way in Linux.