In fact, the idea has been bouncing around since World War I. In 1917, Canadian Prime Minister Robert Borden first proposed Canadian Annexation of the archipelago. (source) However, Great Britain was not amused. In 2004, Nova Scotia discussed inviting the Turks & Caicos to become part of that province. But, nothing has yet come of this nearly 100 year quest for a Canadian outpost in the warmer climates.
But that doesn’t stop the deluge of blog posts and news reports discsussing the potential for the Islands to become “Canada’s 11th Province.” Nevertheless, that seems quite unlikely.
To add a province to Canada, the Canadian Constitution has to be amended. Prior to 1982, this would have been comparatively easy, since there was no amendment procedure in the Canadian Constitution — amendments were enacted by amending the British North America Act of 1867. But, that required that the Canadian government would have to request the UK government to pass such an amendment, but from what I have read, they usually rubber stamped such requests.
Now, since Patriation in 1982, the Canadian Constitution Act, (Sections 38 to 49) requires an amendment under Section 38 of the Act in order to admit new provinces. To pass an amendment under Section 38 requires the House of Commons and the Senate to both pass identical resolutions, and then two thirds of the provincial legislatures must also approve of the change (so 7 provinces). But, those 7 provinces’ population must add up to at least 50% of the Canadian population. Therefore, if Ontario (38.4% of the population) gangs up with Quebec (23.6%) or British Columbia (13.1%) against an amendment, then even though 8 out of 10 provinces are in favor, the amendment would fail.
However, adding a mere territory is permitted under Section 44 of the Constitution Act, which only requires an act of Parliament. This is how Nunavut became a territory (but it is not yet a province). See Nunavut Act of 1993.
What’s the difference? As a matter of law, are largely self-governing (similar to an American state), and territories are run by the federal government. But, the difference between territorial and provincial status has lessened over the years as the federal government has granted territories powers and benefits that are largely the same as that enjoyed by the provinces. (source) However, as you see above, the territories don’t take part in constitutional amendments.
At this point, there are 10 provinces and 3 territories in Canada. The smallest province, both in territory and population is Prince Edward Island, which has about 140,000 people spread over 5.6 million square kilometers. The territories of Northwest Territories, Yukon, and Nunavut are huge, but have 41,000, 34,000, and 32,000 people respectively. The Turks & Caicos consist of a mere 430 sq. km. and about the same population as Nunavut.
Setting aside the unprecedented nature of a “Turks & Caicos Act,” absorbing the islands into Canada at all, it would seem quite unlikely for the islands to join as a province. While the Nunavummiut (for example) would have no power to do anything about it (provided 7 out of 10 provinces with 50% of the population wanted it to happen), Canada seems to take the issue of aboriginal rights and concerns quite seriously. It would seem to be a bit of a slap in the face of the Nunavummiut to grant provincial status to a new entity, while they do not enjoy the same status.
On the other hand, if Canada wants its own version of Hawaii, perhaps the T&C would have some bargaining power to insist upon being a full province or not agreeing to hoist the Maple Leaf over its tropical beaches.
However, I’m not entirely certain that they would push for that status. Being a province comes with more power, but it is a tougher marriage to dissolve. No territory has ever sought to secede from Canada. However, Quebec has a long history of flirting with independence. In Reference re Secession of Quebec,  2 S.C.R. 217, the Canadian Supreme Court held that a province has no right to unilateral secession. But, in the same opinion it held that if a Quebec referendum came out in favor of secession, the rest of Canada would have no basis to object, and the breakaway province and the rest of the country would need to then negotiate the terms of the split. Given the unprecedented nature of the union, I question whether the T&Cs would be interested in jumping right into a constitutional marriage with Canada, rather than trying out the relationship as a territory first.
Even stranger would be the possible “Singapore situation.” In 1963, when Peninsular Malaya and northern Borneo gained independence, Singapore was incorporated into the new Republic of Malaysia. But, two years later, Malaysia decided that it no longer wanted Singapore. The Malaysian Parliament voted 126-0 to expel Singapore from the republic, thus creating a reluctant new independent nation.
Certainly, the T&Cs would like to try out the relationship as a territory. But, what if Canada didn’t like the relationship? What would happen then? If Canada admitted the T&Cs as a province, it would certainly seem to be constitutionally messy for them to then change their minds and expel the islands. As a territory, the Canadian government would seem to have the power to a unilateral divorce. Alternatively, they could leave the Canadian flag up, but devolve as many powers as they liked to the local authorities — creating an independent state in all but name.
If the T&Cs were to become part of Canada, it is virtually certain that their only status would be that of a territory and not a province. Accordingly, if it happened (which is doubtful) it would likely not be “Canada’s Hawaii.” It would look more like “Canada’s Puerto Rico” or “Canada’s Guam.”