Here's how Perry stacks up against six of his peers (stats are from 2006 to 2022 through today):
All three of Kessel, Spezza and Pavelski have more points and more points per game than Perry. All three of them scored more per game in the playoffs as well (Spezza at 0.82 PPG, Kessel at 0.84 PPG, and Pavelski at 0.74 - Perry is at 0.65 ppg). Perry has fewer years as top twenty scorer (3) than any of these three players (Kessel has 5, Spezza has 4, Pavelski ties him with 3). Granted, there's more to hockey than offensive stats, and maybe Perry gets some extra credit for being a power forward, but it's not exactly a compelling start for his HOF case (besides, Pavelski is a far better two-way player).
Statistically, Parise and Perry are very similar. 19 points in 43 games separate them in the regular season. Parise also scored more per game in the playoffs (0.76), though Perry maintained that over a larger number of games. Perry has one extra year as a top 20 scorer (3-2).
Wheeler is more of a playmaker, but he's only 14 points behind Perry. Think he'll catch up over the next 132 games? He also has more years as a top 20 scorer (5-3). They scored at the same rate in the postseason (0.65 ppg), though Perry maintained that for much longer.
Marleau will (probably) get a spot in the Hall due to his freakish longevity (which isn't captured in this chart), and therefore he isn't a good comparable. (Perry, at least as of now, isn't anywhere close to Marleau's totals for games played, goals, or points).
Hardly anyone considers any of these players Hall of Famers (except Marleau, but like I said, that's for his freakish longevity). Perry hasn't separated himself from any of the others (and in fact, is behind many of them) in points, points per game, playoff points per game, and years as a top 20 scorer. He would be one of the weakest forwards in the Hall of Fame.
All that being said - I think it's highly likely (90%+) that he's inducted. The Hall of Fame voters, as far as we can tell, don't do deep dives like this. They'll see his Hart trophy, Stanley Cup, and two Olympic goals(*), and that will be enough.
(*) Good for Perry for accomplishing these things, but a deeper dive shows that it isn't nearly as impressive it looks. Perry won the Hart, but he was fortunate that during what was by far the best year of his career, all the other top players had off years (Crosby missed half the year, Ovechkin had his weird two-year slump, Malkin missed half the season, Kane wasn't a superstar yet, Datsyuk missed 30 games, etc). When the Ducks won the Cup, he was around the 6th to 8th best player on the team - a solid contributor, but not like he led them to the victory. As for the Olympics, he was pretty obviously a minor contributor to the 2014 team. On the 2010 team, his stats look pretty good (4 goals and an assist in 7 games) unless you remember that 3 of his 4 goals were running up the score in blowout games. Believe it or not, I have nothing against Perry, just that his resume isn't nearly as good as it appears at first glance.