Is there a way to use display logic based on distribution channel?

Go to the survey flow and create an embedded data. Click on the blue arrow and see the options available under survey metadata. Choose the one the corresponds the distribution channel you are using.
Put your demographic questions in a block. Add a branch to display these only if the distribution channel ED is empty.

An easier way is to use display logic on the question (since you said a demographic question and not the set of demographic questions). Display logic is easier because you don't have to create blocks and branches etc. I would recommend using display logic based on the contact list email not being empty. See this help page for more detail on display logic.
Display Logic
However, if you really meant a set of demographic questions then you are better off creating a block for your demographic questions and adding branch logic on that block in survey flow like ahmedA recommended.