I know, stupid question. But, if the frost did get my azelea (or any plant for that matter), does that mean that the azalea plant is dead, or that it just won't do anything this year?
Get, in what sense. If it killed the flower buds, no. If it killed the leaves as they were emerging, no and it should put out new leaves. If it was severe enough to kill wood, it depends on the extent of the injury. If the last, I would prune back to green wood.
About the only way frost kills an azalea is if it causes bark split. Bark split is most commonly caused by an early autumn frost while the sap is still high in the plant, or a late spring frost when the sap has already started to rise. For this reason it is dangerous to feed nitrogen to a rhododendron or azalea that could stimulate growth through to autumn. Don't use nitrogen after mid-June. When the sap freezes, it expands and ruptures the tissue under the bark and splits the bark. For this reason always keep mulch away from the trunk of plants. Bark split damage can be treated with grafting wax to prevent fungal and insect damage. If left untreated, it is fatal.
Here is a link that might be useful: Rhododendron and Azalea Troubleshooting