I seem to recall that someone once did a tutorial on placing text on a wine bottle in SketchUp. I wasn't able to find it, but I believe it went something like this:
Set up your curved surface (like a really large-diameter cylinder), but don't make it a component.
Create the text you want to apply to the curved surface using the 3D text tool. Align it with the curved surface so the text is centered on the diameter of the curve, and at the desired height.
Use Push/Pull to push each letter toward the curve until it intersects.
When all the letters have been extruded in this way, select everything and run an Intersect with Model command. Erase the waste (the extruded letters, that is). You should be left with the outline of the letters on the curved surface. Now you can make the curve a component.
I gave this a quick try and it seemed to work. See the attached SU file. Hope it helps.
Best,
dh
curve test.skp
