As near as I can tell, no; Tolkien never addressed why he chose Gondolin as Glamdring and Orcrist's places of origin; the reference goes back as far as the first draft, according to There and Back Again: J.R.R. Tolkien and the Origins of The Hobbit (emphasis mine):
In the original draft of The Hobbit, Tolkien had not fully decided that this Elrond was in fact the same as the Elrond of the mythology. He is described as an elf-friend, 'kind as Christmas,' an attractive alliterating phrase that was later changed to 'kind as summer' to remove the overt Christian reference. And the passage where Elrond identifies the swords is considerably shorter; he knows them to be old swords, made in Gondolin for the Goblin Wars, and he wonders whether they came to the trolls from a dragon's hoard, perhaps from one of the dragons that plundered the city at its fall.
There and Back Again: J.R.R. Tolkien and the Origins of The Hobbit Chapter 10: "Goblin Wars"
A plausible theory is the one given in the question, that Tolkien had a special fondness for the story of Gondolin. However, I personally favour a more mundane explanation: it was just the best story to pick.
In Letter 257, Tolkien mentions the history of the Elder Days as providing "historical depth" to The Hobbit:
It had no necessary connexion with the 'mythology', but naturally became attracted towards this dominant construction in my mind, causing the tale to become larger and more heroic as it proceeded. Even so it could really stand quite apart, except for the references (unnecessary, though they give an impression of historical depth) to the Fall of Gondolin, Puffin 57 (hardback 63); the branches of the Elfkin, P. 161 (hardback 173 or 178), and the quarrel of King Thingol, Lúthien's father, with the Dwarves, P. 162.
The Letters of J.R.R. Tolkien 257: To Christopher Bretherton. July 1964
This is similar to a comment he made in an earlier letter, talking about something similar in The Lord of the Rings:
Part of the attraction of The L[ord of the] R[ings] is, I think, due to the glimpses of a large history in the background: an attraction like that of viewing far off an unvisited island, or seeing the towers of a distant city gleaming in a sunlit mist.
The Letters of J.R.R. Tolkien 247: To Colonel Worskett. September 1963
If the intention of the allusions to the Elder Days is that "historical depth," then Gondolin is the obvious choice; it's easily the most significant of the ruined Elvish cities, and holds a special place in the in-universe narrative structure.