While I have no personal experience either with your particular carseat, aircraft, or AC, I have on multiple occasions had FAs offer to store a carseat for me in the closest when flying in int'l business class (both UA and LH come immediately to mind).
My suggestion: board with it, try to put it in, and, if it doesn't fit, then either gate check or ask if they will store it for you. Worst case you end up gate checking it as you were thinking of anyway.