Is the ocean at either end of the map infinite?

I think people are misinterpreting the question. There are only certain ways to drain the ocean. You can keep pumping from it indefinitely.

Pumps don't work at all because I'm currently draining the ocean using pumps and the ocean is not going down at all. So dig to hell to drain it but think before you do. Get all the shark fins you need before draining it.

1. If your house is over 2000 blocks (4000 feet) you would need multiple wire networks to move the water, as a single wire 'network' can only consist of 2000 wire.
2. Just use an infinite water source if you need alot of water.

No, it is not infinite, see the wiki:

• Players may attempt to drain the ocean by tunneling down to the Underworld, where water evaporates. The Ocean is in fact drainable this way, and this method will allow the player to go back to the Ocean floor and easily pick up all the Coral without worry of suffocating. However, no Sharks will spawn once the Ocean is drained, and previously-spawned Sharks will have vanished. Therefore, draining will not allow a player to obtain Shark Fins and the Diving Helmet.
• Another way of draining the ocean is by making an air pocket, empty a bucket of lava in it and place an object that can't be destroyed by lava in the lava. After that allow the water to flow into the lava. The object will prevent obsidian from being generated, causing all the water to disappear.