It's an interesting idea, but I haven't found any evidence for a common origin in the TV shows, films, canonical sources, or in the EU so far. Of course, proving a negative . . .
I've identified the following appearances of silicon life. There may be more.
Crystalline Entity (TNG: "Datalore", "Silicon Avatar")
Excalbians of Excalbia (TOS: "The Savage Curtain")
Horta of Janus VI (TOS: "The Devil in the Dark")
Microbrain of Velara III (TNG: "Home Soil")
Silicon-based parasite (VOY: "The Disease")
Silicon-based virus (ENT: "Observer Effect")
Silicon-based Lifeform mentioned by Hirogen (VOY: "Prey")
Possible silicon-based Lifeform Kessok (fan fiction, non-canon)
Possible silicon-based Lifeform Brikar (various novels)
Tholians (several series) Somehow omitted originally. Thanks, sfhq_sf!
Given the radical differences in anatomy across the group of known and possible silicon beings, it would be hard to argue that they were all seeded by one progenitor species. For instance, the Horta and the Crystalline Entity are so different in so many ways. Could some of them be related in that manner? It's possible, but I see nothing to indicate it.