Do you mean simply that the lowest volume setting (one above mute) would be louder than if fed its rated input?
Also, what happens when you use a 2Vrms DAC output with an amp with an input sensitivty of say 1.5Vrms? Does the amp simply reach its rated max output at a lower volume control level, and then clip after that (whereas it wouldn’t clip if fed 1.5Vrms)?
Yes, a high level input (considerably above rated) will mean you will get all your volume rang in a small rotation. Right near the lowest point it may be louder than you expect. Also, conventional pots track (L-R) very poorly down that far.
HiFi Amplifiers (generally) have a fixed gain with an attenuator up front to scale the input voltage to the following stage/s to give a semblance of level control.
D/A converters (generally) have a fixed output level for 0dbFS. Back in the earliest days of CD, before the machines had even hit the market, the 'standard' was set at 2.0V (after being revised up from a previously agreed output of 1.4V (see below post). There are various reasons for this, not the least of which was marketing and a desire to get as bigger S/N numbers as they could and also be able to actually use and demonstrate the full 16bit capability of the format.
https://www.audiosciencereview.com/forum/index.php?threads/sinad-measurements.4071/#post-95590
A 2V (at 0dBFS) rated D/A converter into a 1.5V rated sensitivity amplifer would be a reasonable match, depending on the type of content you listened to. Heavily compressed modern recordings where the peaks and averages are within a few dB of 0dBFS would mean your amp would be unlikely to over driven regularly, just sometimes. A fan of wide dynamic range classical music however would be left wanting as the output would be insufficient most of the time and only 'right' at crescendos. That said, it'd be a safe option.
A typical 2.0V rated output digital device is fine into anything from 150mV to 1.5V as long as you exercise judgement with the volume control. Bear in mind, there is nothing wrong (and a whole lot of right) in having a volume control up near its maximum if your levels are appropriate. S/N is often very much improved near max position.