No, you can't delete that folder, since you would also delete all the files
referenced in it. You can, if you are interested in privacy, 'encrypt' the
data.
Rightclick the "Indexed Locations" folder, properties, Advanced tab, see
checkbox for encryption. (This would mean ONLY the user signed in with that
ID/Pass would be able to see those file names.)
If you use encryption, you need to have a password, and create a 'password
reset disk'