For an a/c crossing the base of an airway where the base is expressed as a flight level, the books only refer to the a/c or pilot. There is no reference to atc crossing at this point. However, when I was doing this under the old bravo one, we used to continue to give whatever radar service the a/c had agreed with us.
The a/c is not under radar control, because the pilot is entitled to cross at this level without any type of service whatsoever in any flight conditions!
The a/c flying on the airway at the base plus 500' is where the problem arises and this where you can have some fun on oral boards!!
I know this doesn't really help, but some things in life are just not black and white, and while there is not a radar crossing service available to every a/c on every airway, there will be rules such as this one to allow people to achieve their goals.