Have been to the Giants Clubhouse a handful of times and Yankee Pier once, never been asked for my boarding pass. I have only ordered takeout.
Giants Clubhouse: wait at the entrance for a hostess to ring up your priority pass card. you may have to wait a few minutes as the hostess is not always there. the hostess will take you to a table if you are dining in, or direct you to the bar for takeout. you get a slip of paper to take to the bar to give to the bartender to order takeout and pay additional charges there if your total is over $28.
Yankee Pier: for takeout orders, do not wait for the hostess. go directly to the far left bar and order there. the bartender will take your order and ring up your priority pass and charge you for anything over $28..