Linguists have chewed over this one for a while. More conservative interpretations of the various studies done have concluded that learning a language definitely does make it easier to learn a closely related language, or an unrelated language in the same sprachbund (In this case, Korean, Japanese, Vietnamese, and a lot of a small languages).

As for learning an unrelated language, there haven't been many comprehensive studies, and different linguists interpret the results differently, but personally I think so. If anything, because polygots tend to have developed personally-effective study methods, and also tend to have realistic expectations. I've seen a whole thwack of monolinguals try to take on English or Chinese and quit in discouragement after not obtaining fluency after only two or three months. Something that rarely happens to people who already have a second language.

Well, I learned French and think that it gave certain tools to learn Chinese, such as the understanding of wiping your brain clean to learn and not trying to reason with the language rules. I have friends who examine and compare Chinese to English far too much, and they speak poor chinese because of it. I keep telling them to stop looking at the language from an English perspective and just go with it.