I was wondering if I could have a mesh that's invisible but I can still see the texture.
If I understood this correctly, you want to make your mesh invisible, but show up the texture put on it, right? So you need a texture that's not filling the entire mesh (like a leaf). You need a .png file with transparent background, otherwise it won't work. IF you mean this, have a look at this video: https://www.youtube.com/watch?v=Gi3oFolsPI0
Edit: Or have a look at the idea given by Mr Zak if you don't want to watch the video (Cycles).