No, not always.
When mimicking the speech or sounds made by another person, yes, you gain advantage on your Charisma (Deception) check. You could benefit when you mimic the speech of an Dwarf, or the war cry of an Orc.
When mimicking the sounds made by by "other creatures," no, you do not gain advantage on your Charisma (Deception) check. You could not benefit when you mimic a horse, bird, or the roar of a hydra.
Ultimately it's going to come down to what your table decides a "person" is in the context of the feat. It may be "any creature of type humanoid" (borrowing the implicit definition from hold person, though no rule says it should or should not apply) or it might be "any intelligent creature" such as an Ogre, Fiend, Celestial, Dragon, or other creature with human-like intelligence.
My interpretation would be that it applies only when mimicking humanoids or the speech-like sounds of intelligent creatures. So, you could benefit if you mimic the serpentine lisp of a blue dragon while speaking, but not the earth shattering roar of that same dragon no matter how hard you tried. (Not that you couldn't attempt it, merely that you would get no advantage due to the feat.)
Still another interpretation is that you'd be required to be trying to pass yourself as a specific individual to benefit from advantage. So mimicking the noise an Orc makes when he bellows wouldn't benefit, but mimicking the Orc guard from three weeks ago who bellowed when you stuck him with your sword would gain a benefit. That's an awful narrow reading, however.
There's many potential interpretations here, and none of them are necessarily more or less "right" than anything else.
Ultimately it doesn't really matter as long as you're consistent.