Nope. They can't and that's why US pushed for many years to convince Turkey to contain Russian access to Mediterranean. The moment this occurs, Turkey will have the unconditional support of US and Europe (and NATO) so Russian retaliation is out of discussion. Therefore, the question is will the Turkish government implement such a decision? Why or why not?
Montreux Convention Regarding the Regime of Straits
ARTICLE 20: In time of war, Turkey being belligerent, the provisions of Articles 10 to 18 shall not be applicable;
the passage of warships shall be left entirely to the discretion of the Turkish Government.
ARTICLE 21: Should Turkey consider herself to be threatened with imminent danger of war she shall have the right to apply the provisions of Article 20 of the present Convention. (this clause continues with a couple more paragraphs)
Source: United Nations Treaty Collection (UNTC)
https://treaties.un.org/pages/showDetails.aspx?objid=0800000280166981
https://treaties.un.org/doc/Publication/UNTS/LON/Volume 173/v173.pdf