The professor character also dies for a cause, putting his life on the line by helping Montag. Faber knows what kind of risk he is running when he agrees to supply Montag the help he'll need to escape the city. Importantly, Faber's choice is based on his antipathy for the system that Montag is rebelling against. His sacrifice can be seen as being directly in line with a chosen cause.
One of the problems with Montag's society is that no one cares about anything. People seem more interested in television than life. When Montag discovers the books, he realizes that there could be more to life. He is one of the few people that recognizes this.
I would say that it plays rather a large role. None of the main characters dies for a cause, but people who do die for a cause have a lot to do with Montag's changing ideas. The old lady who died with her books is the main instance of this, though we can sort of put Clarisse in this category as well.