I suspect there is something in it, the very serious guys do it. Generally run them once in a practice session the meet before you want to use them....then shove them under the house.
Most people in the real world don't bother or can't. A qualifying session is generally 15-20 min, and you can't go fast first lap due to the goop on the tyre.
However.....the 2nd and 3rd laps for some tyres are the best they will ever do. So if you were dead serious about time attack you might use new tyres in a morning session if you know the track, and give it a real shot on laps 2 and 3.
Finally....different tyres react to heat cycles very differently- some are hardly affected, some are absolute rubbish very quickly. Yoko A048 are an example of badly affected.