No. Let's consider a very simple hypothetical.

My table has data inserted in pairs of A and B, so the data looks like (each line being a row in a table)

COLUMN
=======
A
B
A
B
A
B
A
B
A
B
A
B

Now I have an index on "COLUMN". That index stores data in order, to it will look like: (each letter being a key in the index)

AAAAAAAABBBBBBBB

Now I delete all of the "A" values for that column.

The table look like this: ("-" is empty space)

-
B
-
B
-
B
-
B
-
B
-
B
-
B


but my index looks like this:

-----------BBBBBBBB

and all that colocated free space will be reused by subsequent inserts.

So a fragment table *might* yield a fragmented index, it might *not*.