I think the market pressure in Montreal is way overblown. Yes, players are better known here than elsewhere. Fans talk about them, media interview them, sponsors hire them, but very little translates to real-life pressure when a player is at a restaurant or walking on the street. "Well-known" is not the same as "Mobbed".
Purely anecdotal, but I've crossed paths with many big name Habs – Lafleur, Gainey, Carbonneau, Robinson, Pacioretty – and never seen anyone do anything more intrusive than nod and smile at them. Usually they're given no attention whatsoever. My friend's son is friends with Suzuki and Caufield – she showed me pics of them hugging her at a party; she calls them "Sweet kids".
I think Montreal players can live their life, eat, shop, stroll, date, without much celebrity pressure. Hockey fans aren't nearly as hysterical as movie star or rock fans. The pressure isn't face-to-face; it's mostly from their social media footprint. Drouin was criticized mercilessly in articles, podcasts, and sites like this one. Gomez had a Goal-Drought website. In that respect Montreal is more obsessive than most other NHL markets. It must be weird for a young player to know people are talking about him online, but with a little experience it's easy to avoid the chatter. Don't read Quebec journals, don't tune into TSN 690, avoid HFBoards, and life is almost normal. Most of the noise is in french, which non-francophone players won't understand anyway.