I don’t recall anyone reporting having used a DEQX with a time coherent speaker (e.g. Vandersteen, Thiel, Green Mountain Audio).
BTW, time coherence implies phase coherence, but phase coherence does not necessarily imply time coherence. Many speakers are phase coherent without being time coherent. See the post dated 7-15-2014 by Roy Johnson of Green Mountain Audio in this thread:
https://forum.audiogon.com/discussions/sloped-baffle
As you've probably seen in the past, though, John Atkinson’s measurements that are presented in conjunction with most speaker reviews in Stereophile sometimes provide impulse response graphs (and associated commentary), and usually provide step response graphs, which can also provide insight into time domain performance.
Presumably the time alignments provided by DEQX would not provide a benefit in the case of a speaker that is inherently time coherent, such as your Treo. But of course the frequency response and room corrections it provides would presumably still be applicable. As well as preamp functionality that is provided by some models, and A/D and D/A converter functionality.
Best regards,
-- Al