Cat 1 approach plates normally have an Loc approach attached to them. The FAF is attached to the loc approach.
CAT II plates do not have anything else on them so don't have one.
It only really becomes an issue if you have some pillock of a TRE in the sim and they decide that the FAF indication has got something to do with the ILS procedure and the FAF is before 4DME 1000ft etc for the approach ban for the ILS. And they start bitching that you have made an illegal approach when the RVR is 500m.
If you get a pure CAT 1 plate where there is no loc approach is approved (I can't think of one off the top of my head) you won't see the FAF cross. You will need to look for a plate which just has ILS instead of ILS/LOC as the title.