If that were the case, then the USSR would have built aircraft carriers in some other shipyard.However, the Montreaux Convention, which gives Turkey control over the straits and regulates the transit of warships through them, prohibits aircraft carriers heavier than 15,000 tons from being sailed through the straits.
Doctrinally, there's a direct line from the MOSKVA class through to KUZNETSOV. MOSKVA is unquestionably a cruiser with a large group of helicopters. KIEV is also a guided missile cruiser with a large air wing of helicopters and some VTOL fighters - doctrinally treated as recoverable, manned long-range missiles. KUZNETSOV has the same guided missile armament as the late KIEV class aviation cruiser BAKU, but with her aviation facilities enhanced to allow the operation of heavier, more capable fighters. Given reports that the missile armament of the KUZNETSOV is being upgraded, I don't think the Russians are keen to move from this doctrine. Interestingly, the design suggests more of a sea control mission for the Soviet aviation cruisers than the land-attack focussed US Navy carriers.
Something similar applies to the INVINCIBLE class aviation cruisers. If you dig down into their design history and features, it becomes apparent that the Royal Navy wasn't trying to pull a fast one and get aircraft carriers by stealth - they're too compromised by the cruiser role.