No officially but for practical reasons they follow what the US does in regards to time. There was no widespread support for expanding the range of daylight saving time during the early 2000s but when George W. Bush changed the start and end dates of DSL to make it look like he was doing something about energy prices, Canada followed along. Given the size and depths of the ties between the two countries, it's impractical for Canada to not be in sync with the US on matters of time.
I think it's pretty safe to assume that a lot of places would follow the US's example if this law passes, and Canada is by far the most likely to do so. I don't think the US is responsible for that, per se, but it's not crazy to treat it as a given that Canada would follow suit.
