Are you sure the WH is not an indirect? This is a tank that is heated by the boiler, not an internal burner. If it isn't an indirect, then yes, you can turn it off in the summer.
Depending on the system you have and how it was installed, a new boiler might save you a fair amount. Back then, the boilers often were way oversized. So, the first thing you need to do is do a heat loss cal to see what size boiler you really need. A condensing, modulating boiler with an outside reset would likely get you a tax credit and/or a rebate from your utility or state.