I believe Toady loads all the images to memory at the beginning of program and only calls those images from memory when needed, removing the need for fetching the image from file each and every time.
Yup, this is how pretty much all games work. They load their content (images, models, sounds, etc.) at the start of the game, or perhaps at the start of each level. But certainly not every frame. The graphics in DF are less than 100 KB, which is negligible.
There is an issue where having many hundreds of images all in separate files can cause slow downs, but this has to do with the interaction between the graphics card and the CPU. Basically, communication between the CPU and the GPU is relatively slow, but once you tell the GPU what you want it to do, it's very fast. When you have all the images in separate textures, you have to tell the GPU to draw the images one at a time, and you end up wasting most of your time on communication overhead.
The solution is simple. You put all the images together in one file. Then you can give the GPU a big list of all the things it needs to draw from that spritesheet. This is the main reason why games like DF use spritesheets. It's more efficient.
The communication overhead is small enough that you can have a couple hundred texture switches per frame without problem, but more than that can have a performance impact.
So basically, adding more tiles to the tilesets in DF won't slow it down.