Where do your materials come from?
AZ in Colorado Springs
Everything can be done using hand tools, or as John describes it, using human power only (and maybe water power).
Cutting a t slot? There were what I'd think of as a specialized scratch stock used to create male & female threads for wooden screws. The same type of device could scratch out the t of a t slot. Wouldn't be quick, and it would require frequently resetting the cutter, but could be done.
Take a walk around colonial Williamsburg some time. They had to add a sawyers pit (which wasn't original) as lumber was brought from another location 15 or 20 miles away. So, to have the hand sawn lumber that's period correct, they had to establish their own source of supply. (I think I was told hand sawn lumber was still available somewhere else a long ways off, and it was too expensive for them.) They have sawyers, joiners, carpenters, cabinet makers, each interesting to visit.
There's a gun shop there CRCwith no electric milling machines. It's not fast, but they cut rifling into the barrels of their firearms with files attached to long wooden "screws."
There are a few guys around who rive their own stock (such as Peter Follansbee and maybe Adam Cherubini) for their projects, but I think most of us get lumber from vendors who derived their stock using modern sources. I think their projects (those who rive or mill their lumber) are "small" -- not much bigger than a breadbox. Probably not a bedroom set of furniture.
So, I think the answer is that you can build a jig or mechanism to carry out any cut or process you can do with power tools. But few people today actually do that. For the historical reenactment that goes on at places like colonial Williamsburg, the various steps along the way are done by many people.
Derek speaks of hybrid woodworking, combining hand tools and power tools. I think everyone who uses power tools is in that category. Who doesn't own a screwdriver and a sanding block? But how many hand tools purists use hand tools exclusively?