I've never seen an ad logged in to Premium. Content creators do sometimes insert sponsor segments directly into the video, but YTP offers a skip feature that works fairly well.
They do sneak it in when a blog etc plays an embedded YT video. It treats that as non-signed-in, you have to stop playing and continue on YT to avoid ads in that scenario.
I've seen ads on the YT app for the nVidia Shield TV in multiple places. Sometimes ad-roll before/during a video sometimes as the first result in a search.