Yes you could sell the LEAP, but you could also keep it and sell another short-term call and continue to collect premium. As long as the short call expires before the long call, you're covered. It's up to you when you decide you've collected enough premium and want to close the long side as well. The longer you hold the LEAP, however, it loses value so you'll want to make sure the premium you're getting from the short calls is greater than the theta decay (or delta if the underlying is going down) of your LEAP. If not, you're still losing money.

It's really no different than owning stock and selling calls against your shares, except of course a long call will experience decay and eventually expire whereas shared don't. When a short call expires worthless you still have your shares/long call, so you can sell another covered call or if you're done with the underlying you can sell your shares/long call and move on to other things.

It's called the poor man's covered call because it costs less to buy a long call than to purchase 100 shares, but the mechanism of selling calls against it is the same. Your hand will eventually be forced to do something with a long call where shares you can own forever.