What does 有节奏地 mean?
Yes 节奏 is a noun, adding 有 making it adjective, i.e. 有节奏的 (rhythmical). And 有节奏地 (rhythmically) is an adverb. 

There are other examples like

有身份(的) (respectable)
有目的(的) (purposeful / purposive)
有人气(的) (popular)