I haven’t done any P4P since before COVID so things may have changed but I never had any issues using coupons. Some soaps can be weird about stuff like that (foreigners pay one price, Japanese another etc) but almost all of the other services were totally fine with it.
Be sure to read the fine print though - lots of times you can only use certain coupons if you’ve never used the shop before, during a certain time of day, only with new girls or girls the shop assigns (no 指名) etc. That always seemed to be a bigger issue than nationality for me.