No. The word was originally a combination of two separate words:
It used to be spelled "threshhold" or "thresh-hold", but eventually the aitches were telescoped.
The word comes from the time when most regular folks had dirt-floored houses. In order to keep themselves off the dirt while inside the house, they would strew a heavy layer of "thresh" over it and would walk on that. This "thresh" was essentially what was left after threshing the wheat and barley (separating the grain from the heads and the straw). Because of traffic in and out of the door the thresh had a tendency to start migrating out the door. To stop this, they would lay either a piece of wood or a flat stone across the door opening. The top of this "thresh-hold" would be higher than the ground, and would stop the thresh from moving outside - and keep water from flowing in through the door, too.
ETA: As @JanusBahsJacquet points out, this may very well be folk-etymology, but if so it's a darned good folk-etymology. I don't remember where I first read about it, and I can't find a source, but oh well.