alt Hacker NewsAlso a Japanese learner here—albeit a beginner. As I understand it, the pitch accent is about stress, languages can stress a syllable with length, volume, pitch, etc. Spanish uses vowel length, Icelandic uses volume, English uses a combination of length and volume, and Swedish (just like Japanese) uses pitch. Just like in English if you put the wrong stress on the word it can range anything from sounding foreign to being incomprehensible. (Aside: I always remember trying to say the name of the band Duran Duran to an English speaker, while putting the stress on the first syllable like is normal in Icelandic, but my listener had no idea what I was saying, it took probably 30 attempts before I was corrected with the correct stress).
I think Japanese is somewhat special though for a large number of homonyms (i.e. words that are spelled the same) so speaking with the correct pitch becomes somewhat more important.
Somewhat more important, but as someone with decent Japanese who knows about pitch accent but can barely hear the difference in real time, and never actively learned it except for the few well known examples like bridge/chopstick, I don't think it matters all that much. Yes, you'll sound foreign. But you'll be understood nevertheless, in the vast majority of cases.