UK version: As you're passing through your busy airport's of choice controlled airspace, your squawk will tell the local controller who you're on the radio with, as a result of which your friendly FIS controller will make you aware of the fact that you might not be exactly where you thought you were.
A FIS implies a non-radar service. I know London INFO assigns a generic squawk (1177 wasn't it?) to all aircraft under their control, but that's not implicit in a FIS and also doesn't mean automatically that London has access to radar images. Do all other FIRs in the UK (Scottish for instance) have the same policy BTW?
In any case, the only thing another controller sees is a 1177 squawk entering their airspace. They need to inform London, and London then needs to figure out, from their flight strips, which aircraft it might be. Before the proper aircraft is found (squawk ident and so forth) might take several minutes, particularly if there are multiple likely candidates.
But in any case if you're being given a FIS, the controller has no way of knowing directly that you're about to enter controlled airspace. They need to be informed by someone else. Unless of course if the controller secretly has radar and performs a RIS-like service, while you asked for a FIS.
Elsewhere, a FIS is for all purposes what the UK for some reason calls an RAS, and they'll bark instructions at you as needed to keep everyone happy.
That still requires radar coverage. Have to admit that that's pretty good in Europe, but not a guarantee. If you want such a guarantee, ask for a RIS or equivalent. No radar coverage, no RIS but FIS only. Simple.