It would be hard to answer this without some further clarifications -- do you meant that he was impressed (pressed) into service on a naval vessel? Canada had become a dominion in 1867, but the Royal Canadian Navy wasn't formed until 1910, so if your ancestor was impressed it would likely have been into the British Royal Navy. Canada was a British dominion after 1867 and the colonies were British colonies before the Constitution Act, so part of Britain either way.

The problem with your timeline, though, is that impressment per se was used by the British during major crises of the 18th and early 19th century (although the roots of the practice date back to the English navies in the 14th century), but the impressment of men for naval service would have ended after 1815. Also, if your ancestor had run from the navy, he would have been a deserter and highly sought after by authorities.

It sounds more likely that your ancestor was shanghaied onto a merchant ship. Sanghaiing was a practice where "crimps" would recruit sailors onto merchant ships, sometimes by literally knocking them out and forging signatures on a muster but other times by using various other coercive tactics. Shanghaied seamen would be bound to their ship for the duration of a voyage, but would be "free agents" after then if they were able to escape that ship's discipline. This sounds like a much more likely scenario for your ancestor.

To answer your more general question, yes, men who were impressed into the Royal Navy were paid. They would be entered on the ship's books at the rate they seemed to have attained (different rates of seamen had different rates of pay). Impressment was intended to furnish seamen for the navy, although press gangs sometimes stretched that definition during times when manning was a serious problem for the navy.