Poloniex will undoubtedly surpass Binance and Bitfinex as the largest exchange if they allow U.S. residents to register and buy crypto on the site again.
I don't think Poloniex ever shut down registrations like Binance or Bittrex did. They did institute a pretty invasive KYC process for new customers last year, and they made KYC mandatory this year, but they never shut down registrations. That said, I don't know how long it takes to get verified before you can start trading.
Now the only thing for them to do is to accept and adopt SegWit-enabled wallets, deposits and withdrawals.
Poloniex has been batching transactions for years, and they've always offered significantly lower fees than virtually all other exchanges, so this isn't a big deal to me. When you get down to it, the real issue for Coinbase wasn't Segwit, but inefficient wallet infrastructure and no batching.