Not yet. It's worth noting that the OneWeb constellation of small satellites is going to be produced in a new factory, because existing ones aren't set up for assembly-line production:

http://spacenews.com/oneweb-satellites-to-settle-in-explorat...

https://en.wikipedia.org/wiki/OneWeb_satellite_constellation

This means that existing companies that build telecom satellites need to do it a new way for these constellations of lots of small satellites.

>> Do SpaceX build telecommunications satellites?

They have a satellite division which has a bunch of people designing things, but they have not launched their own yet. They have also made known their intention of fielding a global internet service via a large constellation of satellites. This application would be a step toward that goal.