I have a similar set of coring bits to UrbanWild and they are a great buy. I have turned many thrift store finds into plant pots by just spending a few minutes with the drill, the bits and and some water to keep things wet.
The way UrbanWild describes the process is pretty much how I do it. The trick is to use the coring bits and to let the drill bit do the work - aside from potential damage to the bits if using too much pressure you also increase the risk of pot breakage enormously.
And yes, it is clearly possible to go without drainage holes, but it means a lot of extra care is required, that can generally be avoided by a few minutes worth of drilling and spending a few dollars on some coring bits.
