Probably, according to this recent research--unless, of course, you do not have quite the right genetic profile (without the correct BDNF balance), are a little too old, are a sedentary male, or some combination of those factors.
According to the summary, if you are a rat who is ADHD, that is another story, however! I know a couple of those, in fact. There is some research (some of which I participated in as a grad student and have yet to recover completely from) that other "treatments," for example, alcohol, valium, hypnosis, empathy--and a few others, may improve pronunciation, at least temporarily.
So the question is: How do the multiple-modality, directed body movement and rhythmic, dance-like routines employed in EHIEP fit into that framework? Are they closer to push ups, a good massage, a glass of wine or a Vente Carmel Frappuccino? My own read on this from about 30 years of body-based pronunciation work is that there is certainly something to it, that exercise is at least good for enhancing mind-body connectivity, body awareness, concept embodiment, kinaesthetic monitoring of speech performance and staying loose so you can learn.
At least for the time being, none of that seems to hold up too well under close empirical scrutiny. Bummer. I'd better go out for a run.