Not likely, but it most surely will damage the lacquer if you play it more than a few times. However, as with everything vinyl, if your record is dirty...and has in groove debris, that is where you risk damaging your stylus.
Damage no. You may need to clean the stylus afterwards, depending on how many plays, condition of lacquer etc. There were / are some 'longer play' dub plates available but I doubt that's what you are speaking of....
No problems for stylus
Fone has lacquer and told can listen 60/70 times
i listen lacquer made in Abbey road from a demo in italy with vertere,Thrax and WB
Touraj of Vertere,owner of this lacquer , told already listen 250 times with Vertere TT
No. Lacquers are soft and only hold their sonics for a few plays. Maybe you need to closely watch the stylus for build up and make sure to carefully remove any material that collects. But it should not actually harm the stylus.