I've heard that it is possible to take an image on photo paper, either as a contact print or with a pinhole camera, and develop it by using a scanner rather than through the wet process. Does anyone have any experience with this?
If by scanner you mean an image scanner then no. At least not with conventionally exposed photographic paper (if you radically overexpose silver based papers you will get an image of sorts without development, but radically means many orders of magnitude more exposure than normal). Until you develop the paper (or film) there is no image to scan. In conventional development the silver halide coated photographic printing paper (and film) is converted into visible metallic silver in areas where it has been exposed to light. The developer is always in solution, so always wet.
Photo paper is ordinary paper coated with light sensitive chemical. These are crystals consisting of silver combined with iodine, or chlorine, or bromine. In their natural state they resemble table salt except the crystal are much smaller. When these crystals are exposed to light, the chemical bonds holding the crystal together weakens. Normally we only expose film or paper briefly to light. This feeble exposure weakens the chemical bond which remains and holds the crystal together. Once the film or photo has been exposed in this way, it is necessary to soak the exposed materials in a chemical called a developer. The job of the developer is to seek exposed crystals and completely terminate the bond. This action releases the metallic silver and washes away the other component. The now unbound metallic silver is opaque and thus appears black. This is typically the way we obtain a photographic image. Lastly, the film or paper is chemically treated to render the image permanent, then washed and dried.
The use of a chemical developer to do this deed can be skipped. If you can figure out how to expose the photo paper to an image using tons of light, the light sensitive silver crystals will self-reduce. Most papers are crystals of silver plus bromine. Now free bromine has a ruddy coloration. When tons of light play on the paper, opaque metallic silver is formed plus free bromine. An image thus forms on the paper. The combined silver and bromine blend to form a maroon coloration.
I don’t think it will be possible to use a scanner to cause photo paper to self-reduce. That’s OK because you can use readymade sunlight to do this deed. Place objects on photo paper under subdued light conditions. These can be coins, flowers, leaves or tracings on paper or photographic negatives. Best if you overlay with plate glass to keep this all flat. Now take your art work outside into the sunlight. In just a few minutes an image will naturally form. No chemical baths needed. You must admire your solar print hastily because it will soon fade by becoming uniformly maroon. To stop the fading we bath the paper in photographic fixer solution, then wash and dry. Solar printing was a viable way to make prints from negatives for many years in the history of photography.
A scanner can not work as a substitute to film development, you still need wet process for that.
On the other hand it can work as a substitute to printing and enlarging.
When using this hybrid approach (in B&W at least; color is different) you need only a changing bag, a developing tank, a thermometer and a couple of beakers for chemicals. Your whole "darkroom" could easily fit in a small box or closet.
You do away with the enlarger, trays and drying racks, which together take a lot of space.
The end results are not quite like wet printed pictures, but for people who are used to the idea that photos should be in electronic format but still want to play the film game it makes good sense.