Can battlefield triggers be reacted to?

Yes — battlefield triggered abilities go on the Chain like any other triggered ability, and once an item is on the Chain the state is Closed, so players may respond with Reactions (Rule 383.3, 813.1.c).

The catch is that there must actually be a trigger to respond to. Battlefield abilities only trigger when their condition is genuinely met — e.g. a Hold ability only fires if a unit was present at that battlefield when its controller scored the point, so with no units there and no Hold, nothing goes on the Chain and there's no window (FAQ #10348). Also remember triggered-ability targets are locked at finalization, so you can react, but you can't react to a trigger and then have a newly revealed unit become its target.