Is it worth indexing a varchar(32) column of UUIDS where half the UUIDS are v1 and half are v4?

I have a MySQL InnoDB table with tens of millions of rows. Each row has uuid column. They are stored in the standard VARBINARY(16). I was recently asked to add a column to this table of VARCHAR(32) that stores the non-dashed UUID hex.

While doing this, I discovered that about half our UUIDs are v1, and the other half are v4. This means that for the first half, since they were all generated on a single machine, the randomness is a bit lacking (only the left-bytes timestamps are different). On the other hand, the newer half are basically completely random.

Is it worth putting on index on this column? If so, I'm struggling to decide how large that index should be (or maybe even what type of index).