Not necessarily the case. Some teams but not all left their throwbacks with different helmets in their uniform guide even though they knew they could not use them until the rule was changed.
These are the teams that have at least a look or more from their past that would require another helmet to be used... if an * is shown then ey still have said look as an option in official uniform guide.
Bears - Brown or white leather helmet era
Bills - silver or Kelly era Red
Broncos - brown, orange, or Orange Crush era lighter blue
Browns - Previous shade of Orange or all white from leather era
Bucs - creamsicle era white
Cardinals - 50's era red helmets or old leather helmet era styles
Chargers - Fouts era blue, Darker navy era as well
Colts - 50's era blue
Cowboys - 60's era white *
Eagles - Kelly green, White, or 30's yellow and blue
Falcons - 70's and 80's Red
49ers - 40's white, Silver and Red also
Giants - looking through their history they wore brown leather, and white leather too
Jaguars - the black/teal color change ones or the gradient (I hope for neither, but they are options)
Jets - Titan era blue or white
Lions - looking through their history they actual wore red, white, blue and even gold helmets at one point or another.
Packers - they wore brown leather early, blue and gold, green with yellow accents, a pale gold and even white.
Patriots - White *
Raiders - Black
Rams - Red from the 30's and 1949, pale gold also from those early years, and yellow
Saints - different shade of gold (unlikely but is a possible option)
Seahawks - silver, different shade of blue
Steelers - Yellow or white
Titans - White, silver or a lighter blue
Washington - Brown leather era, or yellow.