TL;DR No
Ground can be provided to a receptacle in four different ways:
- Plastic box - ground wire to screw on receptacle
- Metal box - ground wire to screw on receptacle - but note that in this case the ground wire should actually go to the box first and then to the receptacle
- Metal box - metal conduit securely fastened to the box and receptacle automagically gets grounded
- Metal box - ground wire to metal box and receptacle automagically gets grounded
This is #9 on my list of reasons metal boxes are better.
Presumably you have one of the last two possibilities. If you see a ground wire connected inside the box then you have # 4. If you don't see a ground wire then you either have # 4 or you have # 3 but with the ground wire connected on the outside of the box. That last possibility is not ideal because it can't be easily verified that it is a secure connection, but it does work.
Any of these will result in a properly grounded receptacle and, therefore no need for (and in fact it would be wrong) a "not grounded" label.
Keep in mind that not all receptacles will automagically work this way. Your typical 77 cent receptacle (hard to believe that anything even close to reliable can be sold retail at that price, but that's mass production for you) won't do it. But spend around $2 or $3 for a "commercial grade" receptacle and you will get:
- Grounding via the yoke - often called "self-grounding". The instructions should make it very clear.
- Screw-to-clamp or similar method of using straight wires (much easier than getting a hook "just right") that is much more secure than "backstab" connections.
- Generally better construction in many other ways.
Most, if not all, GFCI/receptacles have these features. Check your GFCI/receptacle instructions and it should make it clear whether it has "self-grounding" or not. If it does, you're all set.
There is still the big question of: What was the previous situation?
replaced a 3-prong bathroom outlet
should mean there was a proper ground previously. In fact, one of the main reasons for "GFCI with no ground" is specifically to replace a 2-prong receptacle witha 3-prong receptacle when ground is simply not available. (It makes sense to replace with GFCI in a bathroom whether starting with 2-prong or 3-prong because of the safety benefits of GFCI in wet areas.) So unless the previous 3-prong receptacle was installed improperly (e.g., ground connected to neutral to give the appearance of a properly grounded receptacle), you are likely starting with a grounded metal box and everything should be fine now. But the only way to tell 100% for sure, if you don't see a ground wire in the box, is to remove the box to look for conduit or an externally attached ground wire.