There's not really much on united.com that shows active association. Small stuff, like some of the banners on the top right side will say stuff like "Use Your Card For..". Or when you mouseover the mileage expiration date, it will say something like "thank you for being a card member, your miles will not expire"

With the club card, eventually a club membership will show up in your travel options section, but that takes a week or two.