You can perform a constant positive G barrel roll from level flight, but it involes more than one G on the pitch up, less than 1 G (but more than Zero) over the top, and more than 1 G on the recovery.
A true barrel roll should not go below 1 G. Even "over the top" (which is really more like "across" the top at [30 to] 45 deg nose high and [30 to] 45 deg heading from base course), approx 1 G is maintained to pull the nose across, continuing to [60 to] 90 deg from base course when inverted and at the horizon. Barrel rolls can be done in formation without the wingman ever having to go below 1 G.
Again, differences in airplane performance may dictate deviations from the traditional "true" barrel roll, which is a roll in 3 dimensions about a point on the horizon 45 deg off base heading. While some may go below 1 G across the top, they should ALWAYS have positive backstick displacement referenced from the trimmed pitch position at entry speed.
To keep it in the context of transport category airplanes, it is more likely a 30 deg reference point would be used, keeping max pitch to +/- 30 deg instead of 45 deg. A faster roll rate would be required, but less pitch authority, initial airspeed, and G.