No, not appreciably.
Think of a memory chip as a bunch of levers on a wall. You can raise and lower levers to encode information, but you’re not really changing the mass of the levers, just whether they’re switched on or off.
Due to the fact that the “levers” in this metaphor are transistors, which are switches that are opened and closed using an electrical current (and the thing they’re switching on and off is an electrical circuit) there is a slight increase in mass due to the flow of electrons when the circuit is on. However, this would be like saying the switches in my metaphor became more massive because your hand deposits some oil on the handle. It’s technically correct but kind of missing the point.
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