Yes, shoes can help alleviate the symptoms of Achilles tendonitis and help treat it. Proper footwear should reduce stress on the Achilles tendon and provide support and cushioning to the foot and ankle.
This includes arch support, a slightly elevated heel, minimal heel-to-toe drop and a good fit, not too tight and not too loose.
Note that other treatments such as rest, ice, physical therapy and medication may also be necessary, depending on the severity of the condition.