.The Fuqahaa have stated:
If the Shafi’ee Imam makes a general intention of witr salaat, it will be permissible to follow him. However, if he makes an intention of performing sunna or nafl witr, he cannot be followed. Generally, muqtadi’s are unaware of the intention of the Imam. Hence, Ihtiyaat will be to perform salaat individually
In the shafi'ee madhab. if general intention is made then that salah would still not be accepted as wajib. so there would still be a problem. the intention of a fardh has to state three things. 1. the thing you doing (usalli) ; the type of salah (dhuhr, subuh); & you must mention fardh. so i would think it would be impossible for the Imaam to intent a fardh for a general intention because he would have to say "fardhan" in he's intention. A general intention will only be valid for a sunnah salah. we can make three rakaats in one go though but it still wouldnt be sufficient. i would suggest the brother team up with a few others & make the last few rakaats of taraweeh together & then the witr.