probably not. we were told by a nursery that we should never cut into the old wood ,but if azaleas need pruning to only prune them back by a third hope this helps
lorraine

If it's an evergreen, (indica) go back to where the new wood comes from the old. There are usually plenty of dormant buds in this area. Make your cut about a centimetre into the new wood side and keep any leaves in the area. You'll need to keep it shaded until about May next year, and misted, or covered with a damp light cloth to protect it from water-loss.

If it is a deciduous azalea, they do come back from old wood, a bit like several Rhododendrons, but it can take a couple of years after being moved for them to feel settled in enough to do this. They take AGES to re-establish roots beyond the ball you transplanted and need all the mulch, wind protection, and spare water to keep the root ball moist (not wet) you can manage - especially over the summer.

If you're transplanting into a shady gully that's reasonably moist/sheltered you can probably skip the fussing. I did the fussing for a 2m mollis in the middle of a dry spell and it lived to both tell the tale and flower cheerfully. The last evergreen I moved was at the beginning of winter, so I didn't need to fuss beyond putting a big rock on the root ball to stop it lifting in the wind.