@williewonka
Yes. This non linearlity as measured by Soundstage affects dynamic range directly. Acting as a limiter or compressor to the louder sounds. The Speaker will sound dull boomy and congested - nearly all speakers do at louder levels - Soundstage readily admits that the majority of speakers have problems with this test.
Group delay is important - especially in bass where many resonant designs have excessive audible group delay in order to deliver more bass output - however this is not so much a dynamic range effect but a smearing that does muddy the sound.
I n speakers I think transient performance is more related to driver integration, flat frequency response and a lack of coloration or "ringing" from the driver - as a percussion strike has many frequencies that all need to be delivered seamlessly and correctly placed in time. A good test is the waterfall plot - a nice clean waterfall will present transients well and without adding coloration. Electrostatic panels like Quad present transients very well.