I started watching anime after receiving a few suggestions from a colleague, and must say I enjoyed it thoroughly. From funny and relaxing slice-of-life series over mecha and fantasy romance to horror, it's made me both laugh and, yes, cry (and I'm an adult male). Soon enough I started learning Japanese with the intention of eventually being able to watch without subtitles... But ironically, because of that I ended up spending my time studying instead of watching.
It's been three years since then, and while I do still watch anime from time to time, it's very infrequent. On the other hand I continue to practice Japanese reading and listening daily. It's become such a habit that I can't stop, even though I have little practical use for the language. Unlike some others I've fortunately not been infected with
yellow fever - I have absolutely no plans to go to Japan for any long period of time, let alone move there and/or find a partner. The culture is too different, I could never fit in!
So yes, anime has kickstarted this long-term project of learning the language for me, which has now become self-sustaining through "you've come this far, you can't stop now", the sense of accomplishment when I notice how much progress I've made, and plain interest. I'll probably continue even if it takes so long that by the time I actually could watch any anime without subtitles, I've lost all interest in anime.
But other than that the effects have been limited I think. I'm fully aware that even "slice of life" series are overly dramatic and completely unrepresentative of real life. And you won't see me enthusiastically talking about it to someone (even if they were into it too) or visiting conventions.