Yes, it is possible. Many systems, particularly older ones had low pressure switches set at lower pressures than current systems. This allows the compressor to continue cycling when there is still some refrigerant in the systems, but not enough to cool things down.
Additionally, odd things, like a clogged orifice tube have the potential of making the system think it has enough refrigerant, but the cooilg cycle is interrupted.
Not too common, but not impossible.
BTW, here'* a project '78 Z28 near me: