If you choose your area carefully, you should have no problem. Like, downtown or anything West of boulevard Saint-Laurent is mostly populated with people who are either bilingual or anglophones. Avoid the suburbs, the entire Eastern portion of the island along with the Plateau and you should get by without problems.
Nowadays, Montreal is almost evenly split between francophones and anglophones. Plenty of people don't speak French and get by, but you'll get the best experience if you aren't close-minded about it. I'm a native francophone and I just love the kind of language-mixing conversations I get with native anglophones or bilinguals. I love practicing my english and the opposite is true for many.
You can absolutely live in Montreal while speaking only english, but it doesn't mean you should remain that way.