I have some with an indication, some without. When provided, it is sometimes combined with the probe detection feature.
So if either the fuse is blown, or the + probe is not in the correct mA or A socket, an error indication and tone appear when the meter is set to mA or A.
If the probe detection also works the other way, i.e. an error indication if the + probe is in an amps socket with the meter set to a different mode, it can give warning before the user makes a connection mistake that might blow the fuse.
These probe detection features rely on a split pin inside the amps sockets, so they work even before you connect to the circuit under test.