Yes it would be possible but because of the way I've set them up in the description the higher the rank the stronger the need to find a mate would be. Lycans operate almost completely on a checks and balances system. The males alone would be extremely violent and ruthless while a female ruling alone would be subject to constant harassment and they aren't keen on punishment or extreme amounts of violence, they also tend to be a bit more abstract as opposed to a cut and dry logical male. Don't get me wrong they are no frail flowers but the pack would demand she find a mate or she could be challenged for the position by a male and that would not go very well. Some of the males are nearly twice the size of the females and because they're unmated they will kill to win. Plus an Alpha would be required to remain with the pack as they are sort of the glue that hold the pack together. Without them the pack would simply disperse and become parts of other packs.
A Beta ranked female would be a better option, still a high rank, one that they can obtain by themselves. Also they would be allowed to leave the pack for the extended period of time.