Do Arahants experience non-neutral mental vedana?
From MN121, where the Buddha discusses his current practice with Ananda, we have:


  They understand: ‘This field of perception is empty of the perception of the defilements of sensuality, desire to be reborn, and ignorance.
  
  There is only this that is not emptiness, namely that associated with the six sense fields dependent on this body and conditioned by life.’


In other words, the Buddha was fully aware of his present circumstances yet not burdened by craving, aversion or delusion. A meal would be a meal. A mosquito bite would be a mosquito bite. There would be no delusions that wanting more or wanting less would be of any value.

Note that "conditioned by life" does allow for things like avoiding peanuts if one is allergic or taking medicines such as insulin as needed. It also allows for cultural food preferences, since those are often tied to genetics. For example, some cultures tend towards lactose intolerance while others rely on dairy products and that "preference" is largely dictated by genetics. However, I find it really difficult to imagine any arahant expressing a preference for a frappuccino over a latte.