Yes, the cases are identical and only the powder charge is changed. The "advantage" of the 5.56 round is that due to the chambers long free-bore and gradual leade the pressures are kept down in spite of the larger charge in the 5.56.
While there is some difference in case capacity between most .308 Win and 7.62 NATO cases, with the latter being on the heavy and lower capacity side, U.S. made 5.56 military brass is in the same weight range and capacity as commercial brass with the military actually on the lighter end of the range. So, no special treatment is necessary. External case dimensions are identical.