When I replaced my heater core, I did not need to drain the coolant. Due to the leak, there was a large amount of coolant sitting in the plastic "tub" that the heater core sits in. I used a black plastic bag to catch most of the coolant, and covered the floor with towels. The carpet has to be pulled back towards the seats so getting excessive amounts of coolant on the carpet really isnt an issue.
Good luck with the install, it isnt that difficult and took less than an hour.
Good luck with the install, it isnt that difficult and took less than an hour.