Struts like those on the SUGAR Volt and SUGAR Freeze have been used on gliders and propeller aircraft without problems. Since they are loaded in tension, they can oscillate like the string on a guitar. Note that they are braced at two thirds of their span to reduce their free length and to increase their resonance frequencies. A coupling between the strut bending motion and oscillating aerodynamic forces can be expected, but only at speeds above the SUGAR Volt and SUGAR Freeze design speed.
Henschel 126 with a very similar strut arrangement. Only with the strut it was possible to reduce the wing chord at the root in order to give the pilot better upward visibility (picture source).
Those struts do indeed reduce drag. They cause friction drag but allow to build the wing much lighter, thus reducing the required lift and the inevitable induced drag.
Modern gliders have very similar wings but do not use struts. This might seem puzzling, but can be explained by the low payload of a glider, which is at most two humans and their equipment. In order to fly faster, gliders use water ballast to make their wings even heavier. Therefore, a glider will not benefit from a lighter wing.
Nimeta single-seat glider (picture source)
In contrast, a revenue-generating aircraft needs to pack as much payload as possible. It cannot afford to carry unnecessary weight around in its structure. Also, a lot of its mass is concentrated in the fuselage, which increases the wing's root bending moment. A strut will help to reduce the root bending moment greatly and will enable a much lighter wing structure.