It will work awesome if you get a really big, wide, sticky tire on the ONE SIDE that's gonna transmit power.
Hope you didn't pay much for it.
Actually, I'd add to the descriptions above. There are a couple of different types of limited slips. The clutch type (which the Ford Trac Lock is ) uses spring loaded clutches to allow a limited amount of slip (hence the name) when you ask the tires to turn at two different speeds as when going around a turn. There is also a Torsen type limited slip (TORque SENsing) that sends traction to the tire with the most traction based on a series of worm gears in the diff. While both types allow the rear end to manage different speeds while turning, they do their work in entirely different ways. As long as the clutch type is functioning properly, it pretty much will split the power to either wheel. The Torsen type will sense which tire has more traction and send a proportional amount of torque to that tire. If both tires have equal traction, it will split the power evenly between the two. The clutch type will over time wear out clutches and require renewal. The Torsen type has no such limitations - as long as it's in good shape, it works exactly the same over time. However, because of the design, the Torsen diffs usually are capable of transmitting slightly less torque than a similarly sized clutch type unit. So there are pros/cons any way you go.
On lockers, there are a bunch of variations. Some sense torque application and lock up as described above. Some can be engaged and disengaged pneumatically or electro-mechanically from inside the cockpit. Some sense a change in tire speed (going around a turn) and unlock, then lock up in a straight line. Lots of variations.
If you want a fairly civilized street car, most folks pick a limited slip rear end. They operate quietly and smoothly for the most part. The lockers can be fairly noisy in operation. And a spool, well, if you've ever driven a car with a locked diff around the pits (making sharp turns) -- it's probably not something anyone would want to tolerate on the street. And in smaller lower powered cars with less robust axles and such, racing rubber can generate enough grip to occasionally break an axle in tight turns in the pits. Don't ask how I know.