Aye, there are indeed such patterns.
The reason the radical 月 indicates body parts is because as a radical it’s also a variant of 肉. Covergent etymology, kind of thing.
And yeah, some radicals tend to lend their reading to kanji - for example, kanji with the radical 工 are quite frequently read as こう. There’s a userscript that highlights when these occur - it’s here
Edit: Oh noes. Leebo’d.