Electrons are almost always paired. When electrons aren’t paired, they are called radicals (at least chemicaly). An anion is an extra pair of electrons.* Alkalinity refers to an excess of OH- in solution. The OH- is an anion made from an extra pair of electrons. In order for this OH- to quench a free radicals the OH- needs to donate one electron in order to make the unpaired electron paired. That leaves you with an OH radical, which is an extremely reactive species that does considerably more damage than the original free radical. In reality, that reaction will never occur because the OH radical is so high energy that making it from anything in your system would be uphill energetically.
The only species that will make an unpaired electron paired, is another unpaired electron. Likewise, the only thing that can destroy a radical, is another radical. Drinking a solution of free radicals would be beyond stupid, since they are what you want to rid your body of in the first place.
On the off chance that your query is simply due to my use of the word quench, all that means is that you get rid of the free radical. If you don’t quench the free radical, then you still have a free radical.
- You can, in unusual cases, have a radical anion, but alkaline water will not have these, since they would be extremely toxic.