No they don't. Very few things get blacked out in Canada when a Canadian channel has the rights. Since CBC does their own broadcast they can't do this, but when a Canadian OTA channel (CTV, Global or CBC (though I've never seen CBC do it)) has the rights to rebroadcast a US program, there is a process called Simultaneous Substitution or SimSub. What happens there is that the local Canadian affiliate asks the cable system to place the Canadian feed on the channel where you would find the American feed normally. Thus, you see the Canadian commercials instead of the American ones.
This does not extend to cable channels though. So during NCAA March Madness, CBS carries a good portion of the games (though to the bane of my existence, the NCAA now lets TruTV, TNT and TBS show games), whereas TSN has the broadcast rights to Canada. This means TSN does their thing, but cannot SimSub CBS as they are not a broadcast network. I would be some upset if TSN could since I get a CBS affiliate from Spokane, where incidentally Gonzaga is based. So during March Madness, the CBS affiliate from Spokane, shows the Gonzaga game in its entirety, good, bad or otherwise. Being a fan of the Bulldogs, I want to see the entire game. TSN on the other hand might start with the Gonzaga game, but if it is a blowout or a more exciting game is happening elsewhere, they will switch. It always annoyed me when I'd be watching one of my favourite teams play and suddenly due to the score of the game, TSN (or The Score) would switch to a different game. Sadly, TruTV, TNT and TBS are not carried in Canada, so I have no option to switch to those channels. Also, March Madness On Demand was blacked out in Canada for the first time last year, so I couldn't even watch it online. I was forced to pay close to $50 for ESPN Player from Britain, as TSN decided to limit their online streaming to mobile phones on their parent company, Bell's network. You couldn't watch on a computer anywhere in Canada (maybe if you have Bell internet perhaps).
This process does lead to a few issues from time to time. Apparently, the cable operator needs 10 minutes notice to change a SimSub. Lets say CBS has college basketball on and following the game Global and CBS are broadcasting the same golf tournament. Global asks the cable operator to SimSub CBS' channel at say 3 PM. However, the college basketball game goes into OT and magically at 3 PM, SimSubbing occurs and no more OT, we are treated to whatever Global is carrying at the time awaiting the golf tournament. Luckily, as a rule they are only allowed to SimSub on the "primary" US network affiliate. So since in Canada, you can subscribe to timeshifting and get a second US network affiliate, you can switch to the other feed and see the OT.
Where most people are annoyed with the SimSubbing is during the Super Bowl. It seems the Super Bowl, on certain cable systems, is SimSubbed on both the East and West US network feed. Since for some reason people watch the Super Bowl, not for football, but for commercials, many Canadians are shut out of the US commercials and instead see badly produced local commercials for liquor stores or some tractor dealership. Thankfully, my cable operator, Shaw only SimSubs the one feed. I watch the Super Bowl for the football, but lots of people would whine here if they couldn't see the commercials.
The oddest situation arises on certain cable systems that retransmit another cable/satellite provider's feed. My parents have IPTV provided by their local phone company (think Verison FiOS), however Sasktel doesn't transmit their own feeds directly from the satellites. Instead, Sasktel retransmits Bell TV (think DirecTV) on their cable system. Occasionally, a program will be airing on an American network on Sasktel, that is also being aired on a Canadian channel at the same time, but is not carried by Sasktel. However, because Sasktel retransmits Bell TV's feeds, but selects its own channels from that feed, it is SimSubbed with a Canadian channel that is not received on Sasktel. Bell TV carries said channel and thus is fulfilling the request to SimSub the American channel. It always annoyed me seeing commercials for a syndicated show I liked and then realizing that Sasktel doesn't carry the channel I am kinda sorta watching.
Now you know more about the Canadian TV industry than you ever wanted to know.