When I move I replace every outlet in the new apartment when I move in.
Apartment owners never swap outlets until they are totally broken down.
So all the outlets IN your apartment are old, loose, and worn out.
Get a pile of $3 heavy duty duplex Pass & Seymour outlets and replace them. I have done so in every place i have lived, all apts.. i am an apt dweller, period.
(this is assuming you are able to physically do this, if you are not handy do NOT try it)
When you do the outlet replacement, add in the standard pigtail groundwire to the back of the box. (drill a small hole or find a small hole in the back of the box, screw down the ground pigtail with a self tapping screw.)
As for worrying about not using power.. Nahh, no problem. The ground is a safety feature in newer codes. It is not 'needed'. IE you will not automatically DIE because it is not there.. LOL.
So do not worry about your amp being plugged in. As long as you are under the total amps for the breaker.. no problem.
And again, if you are not sure about swapping duplex outlets, find a friend who IS good at it.
You do not even have to ask the landlord.. In fact, most will be pretty mystified you want new outlets. so usually asking THEM to do it is not gonna get you new outlets!!
Also, do you have a breaker box IN your apartment?
If not, your allowable amperage is probably pretty small.
Find out how many amps service your apt.
If the box IS in your apt, open it and see haw many various amps your apartment carries.
I will not bother to rent unless the apt has at least 60 amp service, and with a electric stove and air, even more..
The more the better for your stereo..
I remember in college, a tiny efficiency with TWO apts on one 15 amp circuit. If my neighbor would use his hair dryer while i used my tiny microwave, boom, the breaker would open. And since it was in the basement....