Can I paint with watercolor on vellum?

In general water based media doesn't work on vellum since it doesn't bind to the surface. That includes water color and acrylic wash. You're best off using an ink based medium and an oil based glaze that would bind to the surface.

I'm not sure why you just need to work on Vellum though. Cold Pressed papers made by Arches and other companies are best for watercolor and Acrylic Wash work and these are what pros use.

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There are absorbent papers that are transparent. I guess it depends on how transparent you want the paper. There are papers that are similar to lamp shades. They have a degree of opacity but they are absorbent. Finer art supply stores carry this. 18"x24" might be the largest sheet but you have to check. Printing? Would you be printing a digital image that looks like watercolor paint? Or do you want a transparent image on a transparent material? Digital sign shops print full color images on a transparent plastic that is made into a lightbox. These are like the movie posters you see inside movie theaters that are lit from inside the framing of the poster. These sign shops have many other options to print on at that size. Butcher wrap paper is that white paper that comes in large rolls. Schools often have it around. It is used for all kinds of events including signs for games and dances. That is absorbent but this will ripple when the paint is very thin. Even with the traditional tempera paint it ripples.

Actually, I had direct experience in using liquid watercolor (just superconcentrated pigment, I guess) I believe from Dick Blick, on yupo paper, which is pretty transparent, but a little cloudy-looking. You can't touch it without wearing rubber gloves at first though, or your paint will not stick to where the oils from your hands touched it. The paper comes pretty large, but I don't think it was quite that big, and I'm not sure where it was ordered from, but you may be able to find it online??? Good luck!