Oh, you can put ads in your game, even annoying ones. My concern is only the homebrew phoning home aspect you mentioned. Just as with AI art, there are people that will take issues with that, including downvoting your game and leaving bad comments or reviews.
Unless you have compelling reasons, maybe consider if a static promotion build would achieve your promotion goal just as well. You have a title screen and a short period between levels, more than enough time and space to put the promotion.