I've tried this (on a modded 1054z) and while it certainly degrades it's far from flat. However at 20ms/div is does go flat and then at 50ms/div it's back to something reasonable. I guess that the oversampling cancels itself out at 20ms/div.

I used flat in a relative way - that's why I added < 1mVpp - you have to increase the vertical scale to find out exactly how low the amplitude is. On my DS2000, the amplitude of a 3Vpp 10MHz sine wave goes to ~ 1mVpp @ 50ms/div. That's from the low pass comb filter of successive sampling averaging, but the amplitude will be different on the DS1000Z because of the lower max.sample rate (and depending on how many samples it's averaging).

~~I don't know if the DS1000Z is doing 256 sample averaging, but if/when it is, I believe there is a null valley at 7.81MHz which will give almost perfect 0V amplitude (+/- a pixel at the lowest vertical scale).~~EDIT: I forgot momentarily that the DS1000Z max. sample rate is half that of the DS2000, so the nulls, of course, begin at half that of the DS2000. The nulls for 1GSa/s @ 256 samples averaged are ~3.9MHz and it's harmonics. Anytime the DS1000Z might be averaging to 12 bits (regardless if the rate is lower than 1GSa/s), you should have a null (0V amplitude +/- a pixel at the lowest vertical scale) at that frequency.

You can calculate the -3dB BW in High Res (if you know the number of samples averaged) by 0.433*(sample rate/samples averaged). You can reverse-calculate the number of samples averaged by finding the -3dB BW first.