Does electrolysis of water alter the electrodes?
It depends on the substance you have used for your electrodes. If they are in platinum, they will not be altered. If they are in carbon (charcoal, graphite), they will not be chemically tansformed, but after a while, they will be slightly corroded, and some powder of charcoal will progressively appear under the electrode on the ground of the flask used for the electrolysis. If they are in copper, there will be oxidized and a chemical reaction will occur at the anode. The copper metal will be oxidized and transformed into $\ce{Cu^{2+}}$ ions, which will produce a precipitate if the solution is basic or contains an anion like phosphate or carbonate. If the electrodes are in iron or zinc, the anode will be quickly corroded and transformed into the corresponding ions. In the beginning, the cathode will not be altered, but in the long run, they will also be corroded, specially if the solution is acidic.
Anyway you have not described the composition of the electrolyte. Common metals like iron and zinc are altered by acids, with or without electrolysis.