You can get a good workout, but it gets very tricky when you do exercises that involve sufficiently heavy weight - namely, the squat and deadlift. These are two of the most effective and important exercises you can do, but it does not take long before even relative newbies require weights on these exercises that are impractical (or impossible) with dumbbells. Hell, the first time I ever tried deadlifting I pulled 225lbs, which is close to the max weight you'll ever be able to use with dumbbells, and I'm far from a "gifted athlete". Dumbbells are also less than ideal for many other exercises: for example, getting into position for the OH press can be tricky, and any sort of olympic style lifts (clean, snatch) are pretty uncomfortable.
So, if you have no other choice, then yea, use the dumbbells and you can still get a great workout. Otherwise, barbells are the way to go.