Welcome to the board!
That sounds very like the scenario in Red Storm Rising when a force of Soviet Tu-95 and Tu-16 and Tu-22M bombers attacked a Franco-American carrier force consisting of Nimitz, Saratoga and Foch escorting an amphibious group to Iceland. The task force was located from their radar emissions by the Tu-95's who relayed the information to the strike groups. One group consisted of Tu-16's armed with obsolete Kelt missiles that had radar transponders to make them mimic the Tu-16's. They were launched towards the task group and succeeded in getting a bonehead of an admiral to send all his Tomcats after the Kelts. While they wasted their Phoenix missiles shooting down drones, the Tu-22M's were able to approach and shoot their missiles unopposed. As there was no fighter cover to thin out the incoming missiles, they saturated the escorts and succeed in sinking Foch and severely damaging Nimitz and Saratoga so much that they were out of the war for several weeks.
Your scenario seems very plausible but in real life I don't think the USN would be so obliging as they were in the book, they've probably been through similar scenarios in training. It also showed something that's been discussed earlier in this thread, namely carriers, especially Nimitz class carriers are designed to take a huge amount of punishment and are very difficult to physically sink. But you don't need to sink it, depleting it's airgroup or getting a hit on the flight deck can put a carrier out of action for a time and that can tip the balance in your favour.