Not a good idea. The problem isn't really with the type of glue or even with glue vs. wallpaper paste, but with using wrapping paper. I once considered the same thing! But the two papers are not interchangeable. Wallpaper is not just thick giftwrap; it's paper that's been sealed and so is safe to use with water-based adhesives without risk of bubbling or distorting. Unless the paper you've chosen isn't 100% paper, you're going to encounter issues, especially if your walls have any sort of texture. It's like gluing magazine cutouts to paper with Elmer's glue: they always warp! I think that's why gluesticks were invented: low water content. Water and paper don't mix unless the paper treated.

If you really want to use your gift wrap as wallpaper, then I'd suppose an oil-based glue or varnish may work. You'd have to test it on the paper and see what it does. If it seems okay, then apply a thin coat to the wall and put up the paper with a wallpaper brush. Also, durability will be naught.

It would cost a lot in wood glue for one thing. Paste would stain wrapping paper and look awful.

I want to put up this wallpaper ( actually it's gift wrapping paper) and all I have is wood glue. Will it work, what if later on I disliked it, will it remove easily without damaging the wall? I also saw a recipe to make your own wallpaper paste. will that work better?

Thank you