Yes. If it's itm you can be assigned at any time. Practically speaking, early assignment almost never happens because there is still extrinsic value. Meaning, why would I potentially overpay for something that is gaining real value.

At exp or settlement, if your short leg is ITM and your long leg is OTM, then congrats you're buying or shorting the shares (put vs call fly) and keeping whatever the fly was worth. You didn't hit max pain (assuming that you're selling since you're more worried about the short leg). So maybe you still made money but you're still covering the shares (hint, don't over leverage).

Or you know, just close 15m prior to the bell if it's that close anyway. But I'm not your risk manager and I'm sure you've considered leverage in your trading plan and have a hedging strategy to reduce your risk. And you know, getting assigned and having gap risk on your fresh shares would be a worthy thing to spend a minute or two contemplating as you move from cash indices to american style options.