It is possible; however, not very probable.
The main parameter that dictates what octane an engine needs is the combustion chamber compression ratio. Simply put, the higher the compression ratio, the higher the octane rating.
If the engine has been on a diet of 93 octane all of its life, there could still be some carbon deposits the have accumulated within the combustion chamber. Just because a gasoline has a high octane reading, does not imply that it will burn cleanly. Over time, a significant amount of deposits will actually increase the compression ratio. Will it raise the compression ratio to the point that the engine rebels when it drinks 87 octane gasoline? See my opening comment.