In all our research, we've only found one answer to this question: No! Never mention gifts or gift registries on anything associated with your invitation. You can however provide the website address of your wedding website, which you can link to Honeyfund.com and your other registries. If you don't have a wedding website, see the next question.
Read more about wedding registry wording.
Note: It is perfectly acceptable to include an insert about your registries in a bridal shower invitation. Download inserts here.