I've gone on quite a few sites (thingiverse, grabcad, etc) in search for a coiled tube, but I have yet to find anything suitable. There are a few coils ("springs") but no coiled tubes (i.e. the springs are hollow). Maybe my searching hasn't been good enough! But I was wondering if this is a limitation to 3D printing models?
No, this is not a limitation. You should be able to create a coiled tube in almost every 3D design software package. However, how to do this depends on the specific 3D design software in use.
You'd generally do so by creating a cross-sectional profile (i.e. a hollow circle) and then sweeping it along a helical path. Another option is to first create a spring/coil, and then hollow it out (some CAD packages have a tool/command for this, usually called "shell").