Core memory (ferrite bead), SRAM (4 transistors/bit) and DRAM (1 transistor with a pseudo capacitor/bit) would increase in relativistic weight depending on their state.
The same is true of batteries, ultracaps, or anything that consumes or stores large amounts of energy. m = E/c^2. 1e17 J weighs about 1 kg. That's about the energy of 2 of the large nuclear weapons ever tested.
Let's suppose we have an average largish lake, 100 km^3 or 1e14 kg of water, and we store it at average height of 60 m above a generator. PE=m*g*h. That 6e16 J of potential energy weighs 651g.
In any case, the charge on the device would be negligible in any direction. It's a ridiculously small amount of charge when compared to the overall device, or even the substrate material of the flash memory cells.
Would be fun to do an experiment though. Maybe in 100 years we'll be able to do that.