Only if Canada specifically invites him for one. A state visit is a very specific thing. It means a head of state has invited another head of state, and there will be all kinds of formal meeting and greeting. The Governor General will have to invite him on behalf of the Queen of Canada to make it a state visit.
He could go just for a chat with Justin Trudeau, but that doesn't make it a state visit. Trudeau isn't the head of state, for one thing, the Queen is. Trudeau is only the head of government. State visits really are special extras.
For example, Trump has been invited for a state visit to the UK but no date has been set yet. I'm British so I know how they go here in the UK. State visits are rare - only once or twice a year, usually, and they are planned LONG in advance.
The foreign head of state is the guest of the Queen, he will be invited to stay at Buckingham Palace, he'll have a horse-drawn carriage ride to the Palace (except if it's the POTUS, because the Secret Service won't let him and insists he goes in his own armoured car), there will be a state banquet to welcome the guest and speeches after dinner to say what pals we are (kind of difficult if the guest is the President of China but the Queen will find something nice to say!), formal inspection of troops, exchanging gifts, all of that nice ceremonial friendly stuff.
But the Queen absolutely does not talk politics. She's there to be head of the nation for all of us in the UK (and, in her capacity as Queen of Canada, for all Canadians), someone we can all unite around, and her never expressing any personal views in public is part of how the system works. Undoubtedly Trump will want to talk politics, so time will be fitted in during the visit for him to meet Prime Minister Theresa May at her official residence in 10 Downing Street. He could fly over to do just that, but that doesn't make it a state visit. If Mrs May flies over to Washington to talk to Trump - which she has done - that can't be a state visit, because she isn't head of state.
I remember a POTUS state visit to the UK in the 1980s where someone had a really bright idea. "Reagan and the Queen are both horse-mad - could they go out riding together?" Brilliant - they went to Windsor Castle where the Queen has stables, she lent him a horse, and off they went for a ride around the grounds. The photos looked great in the newspapers, and that was the whole point of it. But of course the real point of that state visit was so Reagan could talk to Prime Minister Margaret Thatcher. The two of them got on incredibly well, it has to be said. They could have done that at other times, and they did - a lot - but a state visit makes it really special.
Maybe it helps to recognise that there is a difference between a head of state and a head of government. I know this confuses Americans because their President is both. Most countries have two separate people in these roles, but the USA doesn't. If you can see the difference, that will help to understand what a state visit is.