No. It expires on Oct 19th (or 12th, if you're using the weekly). You might get early assigned, particularly yesterday due to the dividend, and your shares would be spirited away.
As far as entering that position, $1 above or below the price should give fairly identical exposure, but if you used the $116, while your payoff would be almost identical to the $114, you'll skirt some of the early assignment risk. But take that logic one step further, and the $115 being ATM probably best serves your needs unless you have a specific directional bias that you're trying to neutralize while maintaining long-term gains (absent that consideration, you should just exit the shares position and take on any delta exposure you want directly). There's lots of moving parts to that example (dividend and liquidity, for example).
And, fwiw, I'd take up the other side of your call writing if I had to take one side of the trade (as it stands, I'm holding Nov $120 calls).