I'm not a expert on the term "canon".
But IMO, there is not enough info to say that they are a pairing, or more precise, that they are still a pairing.
Even if they had a sexual interaction, it doesn't mean they are a pairing, or are still a pairing.
Because Gin refused Vermouths offer. Meaning that, in case they were a pairing, that they could have already broken up.
Thus they would be considered a ex-pairing. But is a ex pairing, which is not definite, a canon paring? :V
If Akai and Jodie are considered a canon pairing, because they were together in the past, then Vermouth and Gin can be a canon pairing too But I don't think jodie and akai are a canon pairing, but a canon ex-pairing? XD
And that Conan Drill... I don't consider that as canon. Yes, I know gosho approved it, but it still isn't done by gosho himself, but by other people. Movies are also approved by gosho, but no one considers it as canon. Same with the side stories from goshos assistants. It's not canon, but approved by Gosho.
Another reason why I don't consider it canon is, because the relationship between Vermouth and Gin was labled as "trusted partners" (or similar). But seriously, they don't trust each other. At least Gin doesn't trust Vermouth, since he wanted to kill her if she did something strange. He does respect her tho (but that's probably also because she's Anokatas favourite. And she does have skill in disguising etc.)
That's reason enough to say that the Conan Drill is not Canon. Since there is already something that isn't true.
That Conan Drill, especially the character relationship ANALYSIS, is just a analysis. Like it says. Meaning it points out the hints that were given in the manga.
Since it was hinted that Vermouth and Gin trust each other, it was stated there. But over time, it was revealed that they actually don't trust each other.
So, yeah. In short, I don't take the Conan Drill as Canon, but more like a "summary for the hints given". Which can turn out true in the end, but not because the Conan Drills says so, but when Gosho shows it in the Manga