During depolarization does the inside of the cell membrane become positive?

Yes the intracellular environment becomes more positively charged due to the influx of Na+ ions (or Ca 2+ ions through calcium channels). Ordinarily the cell membrane has a resting potential of -70 mV that is maintained by the sodium-potassium pump. But when the cell is depolarized, the voltage increases to -50 mV, since the sodium influx adds positive charge.