In a video, DJP says that to make roots he uses a random word generator set to fit the language's phonetics.
So it's only a lucky coincidence.
I keep hoping to find more correlations like that. The main problem I'm having with the language as is, is that it's existed in this world with a minimum of corruption to the "Common Tongue" used in Westerns. Maybe it's different in the books, which I haven't read, but on the show, it is very clear that this Common Tongue is English, but it seems completely unrelated to and unaffected by High Valyrian, which seems dubious to me. I'd love to see more correlations like this--although even that wouldn't lay my concerns to rest.
Following a common practice established by Tolkien, the Common Westerosi tongue is “translated” to English, while the other languages are left as-is. It does not mean the Common Tongue is literally English. That would be quite weird, after all, since English is shaped by its particular history on Earth; e.g. the Norman invasion (leading to things like ~60% words being from Latin, or the pig/pork distinction); the Viking influx (leading to things like "egg" rather than the expected ey); the Brittonic substratum (leading, perhaps, to the -self that distinguishes "her" and "helself"), and so on; and of course the history of the Andals is entirely different than that of the English. (That's why it breaks my immersion when the show does stuff like punning on "sea"; there's no reason why a pun specific to English would work in Westerosi).
Since the Common Tongue was brought to Westeros by Andals and the Rhoynar, it descends from some language (or two!) once widespread in Essos; presumably words like Westeros → Westerosi and Rhoyne → Rhoynar, or the -os suffix in Westeros/Essos/Sothoryos/Ulthos, show us a little bit of what this language(s) looks like; just like, in Tolkien, words like Adûni show us a little bit of what Westron looks like. But in Tolkien Westron/Adûnaic is almost transparently "translated" into English, so we don't get to see much of it; and, likewise, in Game of Thrones the Andal/Rhoynar Westerosi language is transparently represented by English, so we don't see much of it either.
And that's why you don't see influence from English into HV. In fact, for reasons of immersion, it's my understanding that David J. Peterson works very hard to not allow visible influences from Earth languages into Game of Thrones languages. A great example is the High Valyrian word drakarys, "dragonfire". One of the few words coined by George Martin himself, he was clearly thinking of a root drac- or dracar-, meaning "dragon", plus another root or suffix showing "fire". But GRRM isn't a linguist, and for DJP this must have felt like a terrible word for a conlang. It's highly implausible that people from another world in another reality would just so happen to name their dragons with a word that coincidentally sounds exactly like Earth's Latin draco or English "drake". But DJP can't erase this word from book canon; he has to work from the books, not against them. So what he did was to create a completely different word for "dragon", zaldrīzes, related to another completely different word for "to burn", zālagon, and also a third completely different word for "fire", perzys, all of them pointedly unrelated to drakarys; which is now transformed into an atomic, unanalyzable word for "dragonfire" exclusively, treated as its own substance distinct from both "dragon" and normal "fire". All of this is done precisely to prevent English (or, more generally, Earth) from showing in HV.