The first part makes complete sense. You will have hotter water water coming out, because every molecule of water has more time in the chiller to be warmed up, so yes, it will be hotter.
However, it honestly doesn't make sense that the cooling time would be shorter. The faster you can run the water, the better off you should be. The thing to keep in mind is that the heat transfer is driven by differences in temp. The closer to the wort temp that the water through the tube gets, the less additional heat transfer you get.
As a though experiment, think about what happens if you reduce the flow rate to 1 gallon per week. Doesn't matter how hot that water gets (and it would come out quite hot!), you're not effectively chilling your wort. On the flip side, imagine you could put an infinite flow rate through your chiller. It would instantly chill your wort, because even if each molecule of water only increased in temp a fraction of a degree, that would pull out so much energy in total that the wort would be instantly chilled to the water temp.