No on a technicality, and no in general.

Technicality: The word territory comes from the Latin "terra", meaning land. A country's territory, therefore, is exclusively those areas of land that a country occupies. Since the Straits of Tiran are a body of water, they cannot be part of national territory.

General: There several major treaties concerning the Right to Navigation on the High Seas. One of the central provisions in these treaties is that any strait cannot come under the direct control of any nation to preserve the right for all nations to use those waterways. In the case of straits, it is particularly important since straits are in many cases the only way to get from one body of water to another and wars have frequently been fought to control straits in the past. While the Straits of Tiran are right off of the Egyptian border, Egypt cannot exercise sovereign power over the straits pursuant to these international treaties.