Does the plant need to be transplanted (moved), or just refreshed due to bare inner/lower branches or progressive branch dieback? If it needs to be moved, spring can be a good time to transplant azaleas as long as the plant can be monitored carefully for watering needs while it gets re-established. If it just could use aesthetic refreshing to make the shrub more full/dense, then yes, you can trim a healthy azalea back significantly and wait for regrowth (it will take several years, due to the naturally slow growth rate of azaleas). You could either do the trimming all at once, or stagger it to remove about a third of the branches any one year, with the process taking 3 years to complete. The latter approach might be less stressful on the plant, and lets you enjoy some blooms (if the shrub is still flowering, at least) while the regrowth matures enough to flower in later years.

It can be difficult to predict how well (and how quickly) any shrub will recover from rejuvenation pruning, but if the alternative is replacement, then it may be worth it to try, especially for cultivars that are hard to find. Given the natural fluctuations in weather we tend to get in early spring, waiting until April or so may be easier on the plant for pruning or transplanting. Bear in mind that any branches trimmed before the flowering period will remove flower buds that cannot grow back for this year's flowering season. Evergreen azaleas tend to expand new leaves after their flowers have faded, so new growth might not appear until closer to May for late-blooming cultivars.

Miri