Not necessarily. If you have indexing structures for data types that do not have a total order, only a partial order, you can store and do an indexed range search on data types that do have a total order. The primary implication is that the output of the range search will not reflect the total order in the way it would for a traditional B+Tree.
The canonical example is indexing rectangles. They have no total order. It is far from the only example. Any data type where equality and intersection are not equivalent test functions will effectively be non-sortable.
There are many indexing schemes for data with these properties. They focus on topological relationships rather than order relationships.