I seriously doubt it, and I haven't seen any interaction between the two. Both outfits have handled their forum presence with professionalism and tact despite efforts by some to stir shit and pit them against each other.
There was a clash between the two some time ago. Zach (Foundation CEO and Co-founder) even made a post in his own blog about it[1]. It mostly started when Matt Odell (seen as an influencer within the crypto community I assume) posted a tweet[2] claiming that all what Foundation did was to clone NVK source code into their product. Besides Matt, even the co-founder and CEO of CoinKite (@nvk[3]) - the producers of Coldcard - was spreading that same information on their Discord channel - that not only did Foundation copied their code but that they were also closed source (you can read more about it on Zack open letter).
I don't know how the situation ended between the two, but I wouldn't be surprised if Foundation (and Zach team) ended up a bit frustrated against this "attack" by nvk and would keep communication on strictly what was needed. You can feel that on Zach closing remarks on his letter:
Our team would appreciate if you lay off the character attacks and untrue statements. Let us know if we’ve done something wrong. But in an open source world, we need to build on each other’s work in order to bring Bitcoin to the masses.
[1]
https://www.zherbert.com/an-open-letter-to-nvk-and-coldcard/[2]
https://nitter.it/ODELL/status/1651220101721358336