This is very interesting and I've been trying to frame a response for a week or so, but it's very complex.

There's two basic things going on with audio systems: Magnitude Response and Phase Response. Each speaker in your system will have a these responses that vary depending on where you measure. Of course we measure where we listen.

Our systems are also linear time invariant, which means if we play a disc today then tomorrow it will sound the same (unless something breaks). This means that the response of each speaker run individually and added together is equal to the response of both speakers run together.

However when we add responses we have to add the combined Magnitude/Phase response (the Complex Responses).

Now, delay is phase. It has no effect on magnitude for a single source. For example, if we add two equal sine waves that are 180 degrees out of phase we get nothing (perfect cancellation). However the magnitude response of both signals would be the same but the phase responses would be opposite and when you add the complex responses you get zero. (This is hard to explain without equations, but I'm controlling myself)

So if you set the delay and flatten the frequency response on each channel individually then we should be happy.

Except I can think of a couple gotchas.

1. If you don't actually look at the Phase Response of each speaker (Does REW do this??) then you have no way to check if you wired one speak in backwards (180 degrees out of phase). Also most people don't really have a good sense of phase and what it looks like in a graph.

2. While we do our best to make the response flat there might be some interactions between speakers that may cause slight perturbation in the magnitude response. For example, if both your mains happen to have a 0.5 dB bump at the same frequency they would add together and might be noticeable under test. Will it be noticeable with real world material? Who knows?

Testing speakers in pairs would eliminate both those. Actually I would pick one and check the others one at a time against the one.