Yes, if your fixer is exhausted, there will be content in the emulsion outside of the image area that the toner will want to alter. The best method for fixing paper, in my opinion, is to use a double fixing bath. One fresh bath and one from last printing session. The 'old' fixer from last session becomes your first fixing bath, and the new fresh becomes your second. Then at the end of your printing session, you can either discard the first bath (now used twice) or you can use it for film (I do this because I use film and paper fix at the same dilution, Ilford Hypam at 1+4).
With film it's easy to test, by checking how quickly it clears a film strip. With paper you can't see this, until you try to tone it, or wait a couple of weeks and watch the print turn yellow. Fixer can become expensive this way.
To make it less expensive, you can use regular fixer as your first bath, and hypo check it all the time, and use a plain hypo second fixer bath. As a first bath, plain hypo won't last long. But as a second bath, it will last for quite a bit.
- Thomas