Yes I think its the best time... I have been in south for more than 1.5 year and monsoon is the best time to visit there.... it will be full of clouds u will be above the clouds.... greenery to its fullest..... but be cautious as sometimes it rains cats and dogs.
June to September: The monsoon season, primarily the months of July and August, can be tricky. However, the beauty of rains and fresh air is best felt during this period. September is a great month to travel because it doesn't rain much and the weather is ideal for sightseeing.
Kodaikanal- also know as queen of hills, is one of the best hill stations down south. Although I visited the place in December, Late june would be good time to travel. With the onset of monsoon the greenery of the place will just let you be amazed throughout the trip.