If I do not give Power of Attorney , will I be able to use broker Pool Demat account to keep my share?

Technically, yes. However, it is not permitted by most online brokers. Brokers are not allowed to keep shares in their pool accounts.

As soon as they receive shares, brokers transfer them to your demat account.

India's settlement cycle is T+2, which means that shares will reach your demat account within 2 working days of your purchase.