Yes they can be propagated from cuttings, but it takes skill. They tend to root but go dormant. The skill is not in rooting them, but in keeping them from going dormant (just sitting there alive but not growing). Before attempting such a undertaking, I would research the proven methods. Basically they involve supplemental light to keep them from going dormant.

Here are some links:

http://www.azaleas.org/index.pl/azpropagate.html#cut

http://scholar.lib.vt.edu/ejournals/JARS/v23n2/v23n2-smith.htm

http://www.arspvc.org/articles/azaleacuttings.html