I have an itinerary which consists of two flights. It's ended up being more convenient for me to skip the first flight and just catch the second. Is this something that airlines will always let you do? I'd call and ask the airline, but it's an Indian airline and, quite honestly, I don't expect them to give me a reliable or comprehensible response.
Nope. If you don't show for the first leg, they absolutely will cancel your booking for the second leg.
More controversially, if you don't show for the second leg, there is not a lot they can do to you, but they will do what they can, including cancelling frequent-flyer mileage and refusing to book you in the future.