If I'm following this correctly, you've used the Text layer as an Alpha Matte to display a texture. And now you wish to add this into the precomp. As long as you copy both layers and retain/reset their layer order in the precomp, that should be fine. From your screenshot, that appears to be the bottom two layers, I'm not sure what the top layer is doing.
In your second post you say you tried adding these two layers, but only the titles of the two copied in,... OH! I think I know what you're saying. What I think has happened is that the temporal position (where their starting point is) has copied over as well, so they are off the comp. Easy fix:
- Select the layers and tap [ this brings their inpoints to the current time indicator.