Yes. You may also note that it doesn't undergo declension (or if someone prefers: its every form looks the same).
Is that because hobby is a loan word? Can you use rozrywka interchangeably?
More than 99% of indeclinable Polish nouns are either loans or Surnames ending with a consonant. But that doesn't mean loanwords are generally indeclinable. I don't know if there is any rule.
Rozrywka is not a synonym of hobby, it means entertainment, amusement. The closest synonyms are probably pasja, zainteresowanie and zamiłowanie do.