It can depend on how big they are, if its a tiny TC (Tissue culture) plant, it might not make it due to not having enough stored reserves, but if its larger and the center of the stem has died. There is a good chance it will pup to replace it. Its worth planting anyway to give it a chance, as long as the corm does not look completely squishy, or hollow if the stem dies down, unless you ordered it though the mail and want a refund. I have had banana plants die down and look dead for months, only to sprout later like a Canna rhizome. Not familiar with your area in Arizona, but I have read some places there like Phoenix are hot and they might need a little afternoon shade, like on the east side of a house, but like Kubali says, it needs as much sun as possible to flower, and bear fruit. Only some wild species like Itinerans (My Musa Itinerans, and Yunnanensis like shade) do better in shady under story conditions. With too much shade, it will probably look a little less ragged, but grow will be slower, but you will have to just use them for ornamental purposes.
Growing Bananas In Phoenix Arizona - Musaceae