Yes you can drift without an LSD. In fact a lot of people who teach people wanting to learn drifting will say you can find the car is a little more forgiving without an LSD (i.e less likely to spin). The only time you'll find it becoming something you need is if your compete and/or you are wanting to link several corners in one drift.

As for wear and tear, this will rise exponentially, if you're going to drift, you WILL break things. Engine wear will be the first of your troubles, but your gearbox, diff, driveshaft (not quite so much), clutch, tires (especially!) and brakes will all wear out a lot quicker.

I don't drift myself, but I have close mates who do compete in the Drift Australia/Toyo Drift Nats and I see how much work they put into maintenance.

A word of advice, you really should know/be prepared to put a lot of work into your car to keep it running. Otherwise, it's a great friendly sport and tons of fun so good luck!