Negative. Hydroboost is for braking. It uses hydraulic pressure from the power steering fluid from the power steering pump to provide BRAKING (not steering) assist.
That is why you look at the firewall behind the master cylinder. You will either have a vacuum brake booster which looks like a round canister, or you will have a hydroboost brake booster which looks totally different.
By the looks of the power steering pump, you likely have a vacuum brake booster. But to be sure, look at the firewall.