Firstly, Nidoking > Nidoqueen.
Secondly, probably not lol. Nidoking loves his sheer force moves, but you're essentially choosing between BoltBeam/both STABs (the former being wiser, since it'l learn Earth Power eventually by level up). Combined with his low BST and average typing, it's very unlikely you could win a single/Nuzlocke with 'em. It'd be plausible if you grind the **** out'a 'King and overlevel him to the point of OHKOing everything, but he's got Medium Slow growth, which is terrible for such a low BST.
Gen 4 and further back, it's a pretty obvious no.