You can definetely drift without a wheel but it's sort of a struggle and really not something you need to be worrying about if you're half-way through a drift. Precision is key, and the analog sticks aren't precise. Know what I mean? Plus it actually helps you drift better in real life, believe it or not, which is something else the controller never really did for me.
Anyway, md0125 is right in that it's not really THAT important, but I do think you should start with a lower horsepower car. Trust me.
Also, I haven't read the entire drift guide but I noticed a few things on there aren't really very accurate. For example, on exiting a drift, you want to countersteer less for a fluid exit. Of course, that alone won't bring you out of the drift, alone it will just make you spin out. But if your entry is good and you are on about the right line, you should start taking the wheel back towards center as soon as you pass the apex of the corner.
Also another important thing to understand is that laying on the gas doesn't move the car in a direction, it accelerates it in that direction. In other words, the effects are delayed. If you floor it until your rear end comes out to about where you want it to be before letting off the gas, then it's too late, you're going to spin out. You have to anticipate it and back off the throttle before it even happens. Some people figure that out quick, but some find it to be a huge barrier, so I thought it would be worth mentioning.