Yes, they can - if they have any Actions remaining, and it's their Action phase, they may play any Action card from their hand they wish.
When you play any action card, you do what you can, and if there's part of it you can't do, you just don't do that bit, and continue trying to do the rest. So for example, you play Jack of all Trades when you have an empty deck and a Watchtower in hand.
"Gain a Silver." OK, I gain a Silver, and I reveal Watchtower choosing to trash the Silver.
"Look at the top card of your deck; you may discard it or put it back". There isn't a top card of my deck, so I don't do that.
"Draw until you have five cards in hand". There aren't any cards for me to draw, so I don't.
"You may trash a card from your hand that is not a Treasure". I trash an Estate.
There isn't any more, so I finished playing the card.
So, you play Band of Misfits and there's no action card costing less. "Play this as if this were any action card in the supply costing less...", you can't do that, so you don't. There isn't any more, so you are finished. You played it, and nothing happened - basically the same result as if you played Sea Hag, Saboteur or Thief in a solitaire game.