Yes. If it is healthy and you are careful when you transplant it, it will recover. It is best to prune the roots slightly and make sure you leave some green leaves.

The conventional wisdom is to only remove one-third of the leaf area, but many people have been unconventional and successful. It is a risk that many gardeners take with azaleas.

Azaleas take years to develop. Don't cut it back unless it looks awful. Even if it looks awful it will fill in on its own if given brighter exposure. There is also the matter of the roots liking to be kept cool, if cut down and moved to considerably brighter exposure may possibly have some problems with roots getting hot. Rhododendrons and azaleas with chronic root rot (and honey fungus) problems seem common in my area, and we do not have the hot and wet summers of the East.

What plants tolerate and what they benefit from are two different things. Shrubs coming back from a hard prune does not indicate they enjoyed it. Cutting back roots after cutting top just reduces plants ability to regrow top. Top supports root growth as well, more top left means more rooting out after replanting. Plants are organisms, like us, do not benefit from double amputation.