Like WisNeuro says, it depends what your professional goals happen to be. If you want to be a PI doing health psych research at an AMC, it is far more likely to be helpful than if your plans are to open a private practice doing family therapy. If its an emphasis in biostats or epidemiology, that will almost assuredly result in better stats training (or at least a better mathematical understanding of it). If its an emphasis in behavioral health - not necessarily. I took 8 stats classes in my program and could have taken more were it not for the fact that I feel like I've largely outgrown the need and am at a point the remaining courses are largely in things I feel like I could figure out on my own. Per my wife (whose has an MPH in biostats), my knowledge of the underlying math is not on par with the typical biostats grad, but my general stats knowledge and ability to apply it would absolutely blow out of the water what even the typical biostats grads can do. I say this not to boast, but just to illustrate that at a research-focused program there will likely be opportunities to build that aspect of your knowledge.
Some other big pluses I think public health in general has going for it are a greater emphasis on policy, health economics and generally "big picture" issues (i.e. reach x efficacy framework - psychology tends to overemphasize the latter and underemphasize the former IMO).
That said, I know tons of psychologists doing public health-type research without an MPH. It doesn't seem to hold anyone back. An MPH is mostly coursework based so its not really going to get you much you couldn't get on your own if properly motivated, it just provides the structure to force you to sit down and read a bunch of mathematical statistics articles that if you are anything like me, would otherwise sit in a "good intentions" pile on your coffee table for months until your significant other complains about clutter and they end up in the recycling bin
Basically, if its highly relevant to your goals and the opportunity avails itself - might be worth doing. I wouldn't go out of your way to make it happen though. Prioritize programs that will get you the training you need for your given goals...whether it be through an MPH in biostats or just lots of extra coursework through the department.