Yes, that's possible. Bargain shared hosting certainly has its limits, and when a site gets very popular, it's time to start thinking about a dedicated server or VPS. It's like trying to handle 25,000 cars per hour on a two-lane road. You can repave the road, straighten out the curves, and put wider shoulders on it, but it still won't be able to handle the traffic.

And there's not much you can do to optimize Wordpress - the folks who develop it have already done about all they can.