Does Indian music have chords?
This is rather difficult to say. In a strict academic sense the answer is yes. There is invariably a melody set against a drone (usually a tanpura) that includes the tonic and the 5th. By definition, the first, fifth, and anything else is a chord. But for all practical purposes the answer is no. Do not try and listen for chord progressions in any classical music. However, the situation may be different with the popular genres. Film songs have absorbed many Western influences. For such Western inspired genres, there may be a heavy reliance upon chords.