It could effect headspacing so you may want to fire form your cases with light loads to bump the shoulder up after doing it. Full length sizing afterwards should be fine since you are sizing the new dimension case.
It could also effect primer seating depth since you could reduce the primer pocket depth. A primer pocket uniforming tool could return them to proper depth but at a cost of case wall thickness between the primer and powder.
It really depends on how deep the stamping is on the case head. Just from what I have sitting in front of me it looks like Remington has really deep lettering, Winchester is really shallow, and Hornady is somewhere in between.
I've only done it for converting worn out .303 British cases to .410 shotshells. The rim is a tad thick on the .303 cases so needs to be filed down. I use pistol primers for the shotshells anyway so the loss of depth is made up for in that way.
Are you doing some cartridge conversions and don't want someone mixing up the ammo? I've converted a couple hundred .30-06 to 8x57mm and just kept the .30-06 head stamps. I don't often use headstamps to verify correct ammo since I prefer to use known samples I keep on hand (and I use a lot of military brass with no calibre markings). I have a pile of .243 and 7mm-08 I have converted to .308, some .30-06 I converted to .308 just to see if I could, the .30-06 I converted to 8x57mm, a pile of .32 Win Special I converted to .30-30, and probably a couple others I'm missing. I keep them all in clearly marked boxes.