Well, this person attests their spoken japanese excelled due to the JSL series. Mind you, they say they spent 3 years covering the series in university.
As for my own personal experience….it’s hard to say. I was only taking Japanese as an elective and just for fun, so I didn’t have any plans to become fluent. I did study hard because I really liked the language, but I gravitated more towards writing. I tried to focus on the listening and speaking more, but the audio tapes absolutely bored me to tears.
Speaking of which, I finally found the audio files on the OSU website.
Give those a listen and see what you think.
If you do end up buying the series, try to find them used. Like here.