This is actually a pretty easy question to answer, if by "sound" we mean the human interpretation of sound waves. In that situation, the answer is a resounding "yes". With that said, I will try to explain my opinion without blathering on too much.....
First, the THD spec with respect to amplifiers and speakers: it is extraordinarily flawed. THD ignores the order of distortion, which is critical to how we humans interpret it. In some testing in the past, it has been demonstrated that some can tell between two amplifiers with a difference of less than 1% THD. However, most are hard-pressed to distinguish between speakers with a difference of 10% THD. How is this possibly a valid metric? Shouldn't a metre be a metre everywhere?
Second, ABX testing: it is good, but far from perfect. ABX testing works well for medium-to-large differences between samples, but in cases where we are investigating the threshold of human hearing it becomes hard to extract meaningful data from an ABX test. There are instances of ABX testing where people have taken the same test 5 minutes later and scored differently. In the test world, we call this low reliability.
Third, measuring amplifiers (and everything else): if two things measure identically in every respect, they are effectively the same. And if they're the same, they will have the same sonic properties and recreate the same physical sound.
Lastly (and most importantly), THE HUMAN EAR IS NOT RELIABLE! It drives me bananas to hear people talk about what they hear and try to associate objective data with what they are hearing. I'll give you an example....I've heard people rave about the "detail" they hear in one speaker over another. Well let's examine what could potentially cause this: 1) Lower Non-Linear Distortion, 2) Wider Bandwidth, 3) A peak in frequency response (ie. linear distortion) that makes a particular sound louder than it is in the recording. Most often, it is attributable to #2 or #3 rather than #1. Anyone that tries to use their ear as a measuring stick for anything is simply foolish. With that simple thought in mind, we can make a lot of extrapolations that all say the same thing: we don't completely understand how we "hear" things yet. Even once we are able to account for all physical characteristics, we still cannot account for the human interpretation. This has been demonstrated time and time again by many in the industry, although Drs. Earl Geddes and Lidia Lee are perhaps the most famous of those currently trying to solve this problem.
So in closing, I must re-answer the question: "Do amps make sub sound different?" Given identical amplifiers in every physical or electrical property, the answer is no, amps themselves do not make subs sound different. Given un-identical amplifiers, the answer is maybe. Given identical or un-identical amplifiers, do we humans interpret the sound differently at different intervals (note that this is a reference to a time interval and not a musical interval)? That answer is yes. This distinction is the crux of this entire argument.