Probably- they were engaged to be married until his death.
While they only officially announced that they were a couple in February 2012, like most relationships, the actual date that their relationship began is a bit convoluted. Check out the link in the description for a timeline of their relationship.
See related links below for photos of Cory Monteith's family members.
No, Cory Monteith was in a relationship with Lea Michele before he passed away.
Cory Monteith was in the episodes, Rehab and The Star
Cory Monteith and Lea Michele were not married, but rumors say they were engaged.
Cory Monteith was on the 5th season of Smallville.
On the show they are known as "Finchel", a combination of their character names; Finn and Rachel