If a computed field is computed at run-time when storageType is set to no, does does the index need to be rebuilt at all as it's all done in memory?
I think you are misunderstanding how a computed field and the storage type works.
storageType has nothing to do with the content being added to the index. It just controls whether the content is stored along with the indexed values. If you store the content too, then you can retrieve the content out of the index. If you don't, then you can only search on that content, nothing is returned in the field value.
A computed field is never "computed" at run time, it is always computed at index time when the value is added to the index.