Not a problem
But I would say that the FAF in some cases is not the point of decent of the ILS it can be anywhere depending on the approach design. In CAT A airports in Europe 99% of the time it is where you start your final approach decent which would be when you intercepted the ILS.
But if you say have a none DME timed procedure to an ILS your FAF is at the locator which you go out bound and start your timing from for the Loc approach and nowhere near the inbound once your actually on the Loc.