The short answer is no. Although there are a considerable number of Gao'uld queens seen in the TV (and non-TV) canons, none are seen to be contemporarily producing live, viable larval Goa'ulds.
The queens seen (or mentioned) in the show are:
- Amaunet - The mate of Apophis
- Anubis' Queen - Not named but seen in Evolution Pt 2
- Cleo - Named by Doctor Jackson. Only seen in fossil evidence.
- Egeria - The founder of the Tok'Ra movement
- Hathor - The mate of Ra
- Isis - The mate of Seth
- Morrigan - Seen in the episode "Summit"
- Nut - Mentioned by Vala in the episode Avalon Pt1
Of these eight, four are definitely Goa'uld larval queens (i.e. as opposed to merely inhabiting female human bodies); Egeria, Cleo, Hathor and Anubis's Queen.
Of these four, none are seen to be producing viable Goa'uld offspring (Egeria and Anubis's queen are producing non-imprinted larvae, Cleo is a fossil and Hathor dies during the process of spawning) which seems to answer your question nicely.
As you've mentioned, we do see some prim'ta (larval Goa'uld) in a variety of episodes ("Children of the Gods", "The Enemy Within", "Bloodlines", "Bane", "Reckoning, Part 1, etc) but we don't see the birth mother of any of them.
For the record, we do see a queen called Anat in the stargate "Living Gods" roleplaying game. She does indeed give birth to live, viable goa'uld offspring but obviously the canonicity of an RPG is highly questionable.