Yes, the sample rate drops as the Delay Multiplier increases, but in a slightly different way to how you’re thinking about it because the Delay knob doesn’t change the sample rate.
You’ll also be helped by making a distinction between the delay time you get (say, 1 second) and the delay knob setting. If you are in 1x mode and have your Rose set to 1 second delay time, activating 2x mode would make the delay time 2 seconds by cutting the sample rate in half (slightly degrading the sound). If you switched to 5x delay multiply, you would get a 5-second delay time with a fair amount of degradation in the audio quality.
So in my example I meant that in 1x mode the delay knob setting was 300 ms, and the delay time I was getting was 300 ms; but if I would change the delay knob to 60 ms and change the delay muliply to 5x mode to also get a total delay time of 300 ms, the scenario in 5x mode would sound more degraded than the 1x mode even though they both had a total delay time of 300 ms.