Do apple watches work with iphones that are with the boost mobile carrier?

Are you referring to the Series 3 GPS + Cellular? If so, see this for the currently supported carriers. Apple Watch - Carriers - Apple

The watches are not locked to particular carriers, however the carrier has to support the watch. Check with Boost Mobile to see if they support it, as there is generally a fee from the carrier to have the LTE on the Watch.

Otherwise, the regular Apple Watches will work with your iPhone, regardless of the carrier, since it uses the phone for its connection. What the Watch will do when the paired iPhone is not nearby, see this. How to use your Apple Watch without your iPhone nearby - Apple Support