No. The integral is reduced by the delta supply actual/return actual. According to your description, the integral would only be counted down once the floor was "recharged" again. But that already happens minutes after the compressor starts.
Okay, learned something new again, and in what context is a higher supply actual compared to a supply setpoint when at the same time there is a spread of 3-4 K between supply and return?
A spread means, conversely, a heat output; if I am outputting heat, then conversely the supply cannot rise higher than it actually should, right? Or is the spread too low? It is usually said that 3-5 K are optimal for a heat pump, isn't it?