Can a vinyl cutter or even just a regular printer be used as a screen printer (like for making t-shirts)?

If I understand your question correctly, some computer printers have the option of printing "Iron on" images using special paper. A "screen printer" I ume you mean silk screen printing here, use one specific screen for each color being applied. It is usually fairly labor and cost intensive to set up a multi-color print station. The screens must be treated with a non-porous coating, not a vinyl applique, in the areas where the color will not go and the colors are then usually rolled by hand, then it changes to the next station for the next color. If the image is rather simple and colors not many, you may setup a simple unit at home. Suggest you search internet for hobby silk screen or such.