Yes. And applies to the whole of North America (and Europe & Asia, too).
Sedges
Rushes

Resin

The definition of a perennial is a plant that lives longer than two years so sedges and rushes qualify under that definition. The only instance where they might not be considered perennial is in areas lower than their accustomed winter hardiness zones - they are still perennials but in these cases, tender perennials treated as annuals. Are you asking if they are evergreen? In a zone 8 climate, most species of both are, but there are a few herbaceous exceptions.

questioner, I cannot claim 'expertise' because I am as confused as anyone on this subject.
Long ago and far away I learned that an 'annual' was a plant which completed its life cycle - it died- in one year. A 'biennial' did the same thing in two years. A 'perennial did the same thing over and over for many years - it did not die quickly. Later, the life cycle part of the definition of an annual was changed to mean 'seed to seed' (not death). Still later the time factor was modified to 'one season'. I suppose that gave rise to summer/fall/winter annuals. Then some perennials were treated as annuals - grown for a short time and replaced. I theorise that theme parks may have started this practice which is now fairly prevalent.
It looks like it all comes down to the practical considerations. If I have an annual bed in my front yard, then I will probably have three or four replantings in a year. Regardless of the classification or health of the plants, they are 'annuals' because of way they are treated. If I am trying to control weeds, it helps me to know that a particular weed will die when spring comes along and I do not have to spray it now. I also know that it will reappear next winter. Botanically it might be an annual but for me it is a (perennial) problem. On the other hand, regardless of what the books (or anyone) say to the contrary, I know that purple nutsedge is a 'perennial' in tropical conditions. It just refuses to go away.
The best I can say is that if the climate is favorable, a plant can behave like a perennial even though it is classified as an annual.