No, the Kinsect's stats only affect the Kinsect.
There are other good bugs out there, but Effect Extender is by far the best...from what I hear. I don't have an Effect Extender Glaive yet, but I mostly use Fleetflammer, which has Speed and Stamina Up (L) and increases Green extract recovery.
FYI, you could've posted in the MH4U Q&A thread, which is generally pretty active.
Edit for relevance: The Effect Extender Kinsect is AMAZING!