merchants may not allow direct-to-merchant (DTM) ppc in their own specific terms, but i don't know of any networks that forbid it. you'll want to be careful here, often, display advertising is more branding oriented (though not always, for sure), so it's conversion rate can be lower than search, meaning your aff margins may not make it profitable. that said, there are SO many different products and services to promote, that there's no blanket "it works" or "it doesn't" here. just saying to tread lightly, ppc can get expensive fast. use the daily spend limit!
networks often do require you to have a site, and sometimes to list every site used, but there are many DTM ppc affs doing this on the search side, and their "do i need a website" situation is the same as those doing display ppc - so it's already doable.