No

The random values for mob spawn times and locations are not taken from the world seed.

Source: My own experimentation. This is super-easy to verify with a super-flat world.

This video tutorial I made (with co-conspirator Kaliard) demonstrates how to make a safe, easy-to-make, and stylish "trash can" incinerator using a chest, a hopper, and a dropper (those last two new in Minecraft 1.5) in a vertical stack, with a redstone clock to activate the dropper. The hopper pulls any items you put into the chest and puts them into the dropper, which ejects the items into a pool of lava in front of it when you throw the switch.

The benefits of this design are safety for you, your pets, and especially your items. There's no worry about accidentally hitting the "throw" key while holding your enchanted pick, as with open-pit designs. Because the redstone clock can be turned on and off with a switch, you can load up the trash can and be sure that, when you flip the switch, only the items that you intend to incinerate will be destroyed.