Totally would work if the neutral is switched, but it's not safe. It means the fixture is always "hot". In the end, it's not likely to cause problems, but it's backwards.

Really this boils down to your switch. Does the white or black wire run to it? Unless it's a smart switch, it will only have one, not both.

As far as adding a on to that circuit, you can tap into whatever is down stream (ie a light) and run a new line (white/black/ground) from that light to your outlet.

You can do the same from the switch itself also, but that's more of a fauxpau