First, a couple of rules that apply on this play:
A batter hit by her own batted ball while in the batter's box is not an out, just a foul ball, as long as the contact is not intentional.
A batter hit by her own batted ball after she has left the batter's box is interference and the batter is out.
Second, there is umpire judgement involved:
Whether or not the batter is in the batter's box is purely a judgement call by the plate umpire.
Technically, what you are describing- asking the plate umpire to check with his partner to see if the other umpire had a better view of the play- is not an appeal. The rule book definition of "an appeal" is very specific and refers to a play where there has been a rule violation that cannot be ruled upon by the umpire until requested by a manager, coach or player.
Batting out of order, a runner missing a base while advancing or leaving a base too early on a caught fly ball are all examples of appeal plays where the umpire cannot rule until a legal appeal is made.
So, strictly speaking, this was not an appeal in the rule book sense. What you did was request that the plate umpire check with his partner to confirm that the batter was either in or out of the box.
A coach may ask an umpire to check with his partner, or get help. An umpire may deny the request. If he clearly saw the play in front of him and is certain of his call, he is not required to check with his partner. On the other hand, if the umpire was blocked out of the play and his view was obstructed, he may seek the other umpire's input.
Also note that, by rule, the other umpire may not overturn or reverse the call of the first umpire. He can only offer what he saw and it is still up to the first umpire to either change his call based on the additional information or stick with the original call. No umpire may blindly reverse or overrule the call of another.
On this play, the original call belongs to plate umpire all the way. He may check with his partner at his discretion, but is not required to. Unless grossly blocked out and having an obstructed view, a plate umpire most likely would not check for help on this play. If he had a good view and is confident in his call, the base umpire would not be of much help. The plate umpire is standing a couple of feet from the play, whereas his partner is 75-90 feet away.
