The simple answer is yes.
Where I am steel screws seem to always be used instead of brass. Usually they are zinc-plated today but on older installations I have seen bare steel used (note: it is common for these to rust slightly, but not enough for any of the screws to fail). I can't actually recall the last time I saw brass screws used for anything other than show purposes, and these days it isn't easy to be certain that you are looking at a solid brass screw when brass-plated steel is becoming more common.
Here are some random images gleaned from the web from around the world showing various steel screws used for this kind of installation:
Steel is actually preferable to brass where there is any real strength requirement — where a part is very heavy or put under stress during use — since brass screws are significantly less strong than steel screws of the same gauge. The reasons that brass is preferable in a marine environment are largely to do with corrosion, and that doesn't apply in quite the same way in a bathroom setting where there's no exposure to salt water.
I'm not certain when you say steel whether the screws in your case are bare, if you're worried about corrosion down the line you could insist on zinc-plated screws or stainless steel being used, but going by common practice it doesn't appear there's any reason to be concerned.