Possible? Sure - many people have flown a C/L model of one type or another with a receiver/servos in the plane and a transmitter hung around the neck or from the belt ... however -

for competition purposes, it would not be legal. AMA competition rules prevent one from using ANY radio control for any functions. The Carrier models you saw were most likely built for competition and therefore any controls were activated by the lines or by electronic signals down the lines (NOTE: it is legal to control things with servos and electronic signals - just not using any type of RF transmitter or through the air signals).

In any case, the functions that you asked about specifically - throttle, hook and flaps - as well as ailerons and some rudder offset, are controlled quite nicely by the 3-line systems that we have available to us. There are some who use servos and down the line signals for throttle but for Navy Carrier we don't generally need proportional control of anything except throttle and elevator, so the flaps and other functions are usually spring loaded into "High Speed" and "Low Speed" positions and actuated either by the throttle line or a quick application of full up or full down elevator.

(Also, note the above posts that mention sport flying is not affected by competition rules if you want to add these functions to sport flying planes there is no reason not to do it, if care is taken not to interfere with other RC units within range).