No, it doesn't count as being married. The law doesn’t see you as married unless you've gone through a legally recognized marriage ceremony in either BC or somewhere else. But if you've lived together as a couple for two years, you're considered spouses and you'll have a lot of the same rights under BC provincial law as a married couple has. If you've been living together for one year, you’ll also have some of the same rights under federal law that married couples have.
For things like health insurance, government benefits (including retirement), and inheritance, you might have the same rights as married spouses if you live together.
If you separate, you’ll be treated like a married couple in certain situations.
When it comes to dividing property and debt, you're spouses under the law and the courts will treat you like a married couple if you lived together for at least two years before you broke up. See Dividing property and debts after you separate to find out more about this.
When it comes to spousal support, the courts will treat you like a married couple if you lived together for at least two years, or if you lived together for less than two years but you have a child together. See Spousal support to find out more about this.
For more information about your rights when you live with someone, speak to a lawyer. See Tips about getting legal help for where to find a lawyer.
Read Living Together or Living Apart: Common-Law Relationships, Marriage, Separation, and Divorce for some good general information about this.
By the way, it might be helpful to know that BC law doesn't talk about "common-law" relationships. You'll probably come across the expression "cohabitation," which means living together without getting married first.