Yes, the House may choose to ignore the Senate when it voices opposition to a piece of legislation. In practice, sometimes it modifies the legislation and sometimes it doesn't change it at all. However, at the end of the day the Senate must approve the legislation or it cannot become law in Canada.

If the Senate refused to endorse the clear will of the House of Commons, there would be much rumbling about a "constitutional crisis." However it wouldn't be a crisis of the written constitution, which assigns equal power in passing law to the Senate. Instead it would be a political crisis, where elected lawmakers express outrage that their unelected peers in the Senate would dare to defy them. The magnitude of that political crisis would depend on a lot of things. In some cases it might not be too big a deal; in others it could be a game changer. Tradition and common sense help to keep us out of that quicksand.