I'm not sure if this answers your question...please clarify if I've misunderstood.
The LabelCurve.CurveId property will get you from a label back to the pipe/fitting/cable tray/whatever. I don't know of any method [aside from brute force -- traverse modelspace looking for LabelCurves with matching CurveIds], to do the reverse. Disclaimer: I haven't done this much -- an obvious answer may be out there for both of us.
-drg