Yes. But it's essentially impossible to do so.
The relationship between CAS, Mach and pressure altitude (FL) is fixed. Therefore if you do as suggested, and
maintains a given Flight Level, and given CAS,
you MUST maintain a fixed Mach also.
I think the problem is that the original text was presumably talking about flying into a frontal system at a fixed GEOMETRIC altitude - in which case the FL won't stay fixed, and there will be a change in Mach for constant CAS. Since it's talking about a case with a sharply delineated temperature profile, changing quite rapidly over a short distance, unless one flew a sudden climb or dive to maintain fixed FL, one CANNOT actually do what the question posits, i.e. fly at constant CAS and FL across a temperature change.
The original article has chosen a bad example to try to explain the difference between CAS and Mach, IMO. They might have done better to consider a constant CAS descent, where they could have talked about the Mach effects just as easily.