Yes
Any event after a player appears at the plate -- even being hit by the pitcher on the first pitch -- is counted as a plate appearance.
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yes. you ground to short with a man on first and they get the force at second... you are 0-1
If scored as a Fielders Choice it will go down as 0-1 (an AB with no hit) -- tigersy2k3
A fielder's choice is always an at bat. The book would be marked as an FC with RBI.