Absolutely. Armstrong is becoming legit candidate for the Hockey Hall of Fame.
I think he locked that in with the 2019 Cup, although he isn't such a slam dunk to put him in while he is still active. That 2019 Cup win made him the only executive to join the double triple gold club (2 Cups, 2 Olympic Golds, and 2 World Championship Golds). By the end of 2019 he had 15 years as an NHL GM and about a decade as a key player in the pro department of Hockey Canada.
He is currently 14th in all time wins among NHL GMs and is just 37 wins shy of 10th. He is 200+ games shy of everyone ahead of him on that list, so his winning percentage is pretty damn good as well. And not for nothing, but the HOF is still very much an old boys club and Army is extremely well connected and respected in that club.
I will be shocked if he doesn't wind up in the HOF, even if he retired tomorrow.
He'll eventually wind up in the Blues HOF, as will Berube and Stillman (we broke the seal on coaches and owners in the inaugural class).
As for players from the Cup team, I think that Steen, Petro, Tarasenko, ROR, and Binner are all locks.
Steen played a dozen years here and has rejoined the organization post-retirement. He was well-liked when here, he adopted a team-first reduced role in the Cup win and he damn near always repped the city with a Cardinals hat in public. 5th in games played all time for the Blues.
Petro was the first Blue to touch the Cup and the photo of him raising it is the most iconic pro-Blues photo in the franchise's history. He led the team in TOI in the Cup run, he was a Blues pick and played 10 full NHL seasons here. Time will heal the free agency hard feelings enough to make him a no-brainer decision for the Blues HOF. 4th in games played all time for the Blues.
Tarasenko played 10+ years here and was a fan favorite for most of it. He was the closest player we had to a superstar in the cap era and his shot was truly the best shot we've had since Hull. 5th in goals and points all time for the Blues and a big part of the Cup run (his 11 goals was 2nd on the team and his 17 goals was 14th). I don't see his exit erasing all that.
ROR won the playoff MVP the same year he won the Selke. Then he spent several more years here and acted as captain. He'll get in based on hardware alone.
Binner's emergence in 2019 was a huge driving force to turn the season around. Then he was super clutch in the playoffs and has been a fan favorite since. He's 32 wins shy of tying Luit for the franchise record and that seems extremely likely since he is under contract for another 3+ seasons.
I think a few more guys have very strong cases, but those would be my 5 where I'd be actively surprised if they don't get in.