Maybe. You will also wait while the heater turns on and heats up in addition to the wait while it comes through the pipes. So quite a lot of cold water is going down the drain until you put the plug in. This can be really annoying when you are cooking and want little bursts of hot water, as the machine turns off and cools down in between so you keep waiting each time. You can have the situation that the water at the hot tap gets colder before it gets hotter as cold water is fed into the hot water pipe, which doesn’t happen in a storage system. For longer use like a shower it doesn’t matter so much.
There are trade-offs with all water heating systems. With storage systems that are gas or electricity you lose heat from the tank which costs you money to replace. With direct solar hot water this loss does not give you a bigger running cost as once you pay for the capital cost the hot water is ‘free’. Storage hot water with an electrically heated tank where you have solar power is another equation as there may be savings heating your water in the middle of the day when your solar system is going strong. This topic is not simple.
