Very true, the base guy is watching the pitcher, the ball and should NEVER take his eye off the ball - especially during the steal. He would follow the ball into second on this play. He should easily see the check swing. He should follow the ball, as if the plate guy called a ball and make his call. Then when asked, he could give his opinion. I agree, the K3 happens first, so nothing at second on the appeal.
My question from the OP is - how did the coach make the appeal to the base coach on a check swing? He has to ask the plate guy to check.