You are actually just pre-heating the water with the plate exchanger before it enters the water heater. You will have to leave the water heater element/burner on to maintain the temp. in the storage tank.
No you will not have to leave the electric water heater on. I have ran mine like this for 5 years, no issues, done well over 150 installs this exact way, no phone calls or complaints.
I was recently away to a funeral, from Tuesday til Thursday, stove was off, electric water hester off, came home and still had hot water, it was likely 10-15 degrees cooler than normal, but still hot enough I had to add plenty of cold to take a shower
Hot water retains far more heat than customers realize, I had a customer who lives in another state have a pump failure last week, his stove sat for 3 days with no wood in it, when he turned it back on water temp was still 144
The water entering the tank is far hotter than hot water heaters are normally ran at, so that gives plenty of room for some cooling should it occur. The only time I'd recommend a side arm would be in perhaps a shop or cabin where hot water was rarely used but still wanted, in 99% of all home applications, it's perfect to use a 20 plate and far safer