I made a test once, playing a sine and recording it with Ot. IIRC it was around 1.5ms.
Edit 2: not sure what was my previous test.
Just made a recording, playing a sine to Cue Outs plugged to INAB and recorded it : the record is around 136 samples late, equals to 3ms.
I added neighbors, used thru and recorded internally, the result was the same.