Does increasing Game Speed count as using cheats in Factorio?

Yes. Using console commands or mods will permanently disable achievements on that save.

As stated in another answer, mods or console commands will disable Steam achievements. Although there's an alternative you could give a try.

You can most likely use a software like Cheat Engine, which will simulate a faster gameplay but probably not interfere with achievements as it's neither a mod nor a console command. The unique speed hack works by simulating a faster tick rate for your game than the game would normally have.

You could make the game ten times faster and everything would be ten times faster. This does mean the in game time will go by faster and you will move faster and the creatures will move faster.

The upside to this sort of hack is that your game will be simulated faster and waiting for stuff will not be such a bother. I used this software for clicker type games where it's really useful.

The downside is that you will be in slow motion compared to the game. So, when a creature that is simulated ten times faster than usual sees you, you will almost immediately die before you can react.

I'd like to add that if you're playing in multiplayer, the speed hack won't be of much use. Also, in case of singleplayer, you should cheat as much or as little as you want.