It is mostly used in combination with a thing or behaviour - not a person as a subject. For example, a confrontation within a relationship of a couple or friends, one would say:
Ich bin es leid, ewig mit Dir zu streiten.
(streiten/fighting, being the subject/reason for being fed up)
Ich bin es leid, dass Du immer Deine Socken liegen lässt.
(Deine Socken rumliegen lassen/your socks are scattered all over the place / is the actual reason for being annoyed.
Ich bin es leid, dass Du immer recht haben musst.
Meaning, that one is fed up of the actual behaviour of somebody, not directly the person itself.
In your example: "Ich bin euch Männer leid" - it is a generalization of the group, which is becoming the subject, again not an individual person.
The basic construction of this phrase is:
"etwas leid sein" (etwas = thing, !not person)
Yes, you can use it the way you suggested, but a native German speaker would not say it this way or at least, the usage of your phrase, the way you mentioned is very very rare.
"etwas leid sein" is not rough or insulting, but it's very straight forward. In business situations in particular, it is common practice to express things more politely. So this phrase would only be used if the discussion is at the peak of confrontation/escalating. Then the "boss/speaker/whoever" would use it to make a hard cut:
OK, ich bin es leid, diese Diskussion hat keinen Sinn.
(OK, I'm fed up/done, this discussion is not leading anywhere)
It expresses the last state/phase of a process, which you are not willing to accept/take any longer. So, before expressing this sentence, you should be aware, that there is no further superlative possible.
If you want different expressions, which are more polite and nice to use, you could make use of:
von etwas genug haben (Ich habe von Dir genug) [attention: can also be positive, expressing satisfaction of the way it is at the moment], negative: Ich habe von Dir genug [I'm fed up from you]
etwas nicht mehr ertragen (I can't stand it anymore)
etwas nicht weiter hinnehmen ( same as last sentence, but just differently phrased )
(very polite/business) mit einem Zustand nicht weiter einverstanden sein (You do not agree any longer)
agressive/offensive: Ich kann Dich nicht mehr sehen