No the tickets will not reach you by mail in time for your trip. The boat is not a reservation-seating kind of thing anyway - just show up and get a ticket and go.
Most of us recommend the local airline instead if you are arriving from out of country. Much easier. The boat can be very crowded and may not be very comfortable - you see more from the air.
If you do take the boat, please note that there are no bathrooms on it - don't drink anything for a while before you get on board - 1 hour 45 minutes of possibly bumpy boat-ride with nothing to be done about it if nature calls. There is a good public toilet at the water taxi terminal.