Crampons can be made to work on trail runners, but I would recommend using strap-on crampons with a more traditional hiking boot. For crampons to work properly, they need to be tight, which is more comfy with the added protection of a boot. Crampons also typically have a strap that secures over the top near where the foot flexes, so positioning the strap on a low-top can be tricky and uncomfortable.
Trail runners with crampons tend to be fine for flat walking and mellow slopes. On Whitney, where crampons really count is the Chute, and I feel most hikers will be better served on the steeper snow of the Chute by using traditional hiking boots with a more rigid sole.
Regardless if you are using running shoes or hiking boots, you really can't afford to be up the Chute with poorly-fitting crampons. A rotated or dropped crampon can lead to a bad situation (see
https://inyosar.com/mt-whitney-multiple-injuries/ for an example from last year of when things go poorly in the Chute). My recommendation is to practice on a snow slope of low consequence first, practice side-stepping and front pointing, etc. so that you know your crampons are adjusted well and fitting properly before tackling the Chute.
