Is it possible to combine spline IK for the body and regular IK for limbs? I've got a centipede model with an IK rig. 
I would like the spine to move along the spline curve in the background, following its curvature, while still letting me pose the legs like normal to make it look like it's running along the wall. None my attempts have worked out - either the body won't stick to the curve properly or I'm unable to move the legs without them glitching out.

Here's a link to an album where I list the methods I've tried so far, including gifs of what the model looks like trying to move along the curve.
as far as your question goes it is possible, it has to be set-up correctly - Where is your 'Spline IK' ??


  I would like the spine to move along the spline curve in the
  background, following its curvature


That would be a 'Path' and could be done several ways 'Clamp To' or 'Path' constraint. The set-up on the legs does not look good to me, your leg bones with the IK should be shifted forward to what is prob the current IK targets and a new or that large bone re=scaled to be the IK targets. That is why the legs are 'Glitching out' on you. I will try and mock up a file for you if you want.
DISCLAIMER: This file created in v2.76 - If using 2.7x it will open fine,, If using 2.8x 'APPEND' the objects from the 'Object' folder.