You can, as long as the gear ratios are all compatible (you can't have any gear being driven at two different speeds or they'll lock). You also have to have an even number of gears or they'll lock (because you'll be turning in opposite directions).
I bought plans for the Simplicity clock a while back but have yet to pull out my scroll saw and dig in. It's a lot of fine detail work and slight mistakes can cause the gears to lock up. But definitely one of the cooler projects for a scroll saw.
What about laser cutting the wood? I'm making a gear clock driven by stepper motors that shows the weather and while I'm handy enough with a scroll saw that I could could probably cut the parts, I went with laser cutting the wood instead.
The other nice thing about the laser cutter is that you can engrave the number/lettering directly onto the parts, though the downside is that the edges will be much darker from the laser burns.
People laser-cut those clock designs out of wood at TechShop all the time. It's really easy, and almost a cliche.
I tried cutting a clock escapement from a wood clock design out of steel plate with a CNC plasma cutter. But TechShop's old plasma cutter wasn't precise enough for that. I could probably do it with their water jet. But after building too many heavy steampunk objects, and lugging them to conventions, I'm sort of over that.
The production and content of the videos are pretty amazing.