No.
A reaction is defined as "a special kind of action" in the rules (PHB, p. 190), and therefore is governed by anything affecting actions. It's special-ness is not defined as to be immune to action-depriving situations.
Furthermore, it would be odd for your extreme lethargy to prevent you from intentionally taking actions, but let up in a flash when you want to take a reaction, and then return.
I understand that Jeremy Crawford rules differently, but his Twitter rulings are no longer official and this has not been addressed officially.
