According to multiple sources as cited by Wikipedia (such as this, or this), the now-under-construction Istanbul Canal would allow Turkey to bypass the Montreux Convention Regarding the Regime of the Straits.
I'm not sure how that is possible. The preamble of the Convention clearly speaks of the
Straits of the Dardanelles, the Sea. of Marmora and the Bosphorus comprised under the general term " Straits "
The same wording, the use of plural Straits, is use throughout the document. Thus, I imagine, the scope of the Convention is broader than just the Bosphorus. Even if there was a canal bypassing the Dardanelles (which I believe doesn't exist, even as a plan), the Convention would still apply when navigating though the Sea of Marmara. Which is exactly where the Bosphorus Canal would lead from the Black Sea.
I mean, sure, Turkey could transfer, or allow the transfer of, ships from the Black Sea to the Sea of Marmara freely, but that's it. I don't see how that would bypass the Convention in any substantial way.
Clarification: I think the point of the Convention is to limit the naval traffic between the Black Sea and the Aegean, and by extension, the high seas. In order do that, the Convention regulates the traffic through three "straits": the Dardanelles, the Sea of Marmara and the Bosporus. With the exception of the latter, the straits would not be affected by the construction of the canal. Traffic through the Dardanelles of the Sea of Marmara would still be subject to the convention.