I think there is benefit to studying a striking style, but if you want to supplement another art, it's hard to do it the right way -- without shortchanging the style. Just so you understand where I'm coming from, I came to aikido after studying striking styles for a number of years, and I didn't really leave those styles by choice -- it was a matter of no longer having a good dojo nearby. Where I live now, there are several schools in various styles that I can't honestly say I have a high opinion of -- they're not really bad schools, they're just not as good as they could be. So, I chose to start all over again in a completely new style. If I had the opportunity to study a striking style at a good school, and I also continued with aikido, I'm not sure that I would do it. If I had the time to train adequately in two styles (3x a week each), I think I might be better off spending my efforts on just one style.
Something else that may be worth looking into is "cross training" in an Asian classical FINE art: Calligraphy, dance, ikebana, tea ceremony etc, there are loads of options. How many martial arts does one need to learn?