"I know that the noisy dog is greedy."
Translation:Dw i'n gwybod bod y ci swnllyd yn farus.
Not in this particular pattern - the second part of the sentence is not emphatic, so bod is required to introduce it. If the second part was emphatic, it would be introduced by taw/mai and it would contain a separate verb:
Dw i'n meddwl bod Siân yn dal - (unemphatic) I think that Siân is tall
Dw i'n meddwl taw Siân ydy'r dalaf - (emphatic) I thank that Siân is the tallest