That's precisely the arrangement I have in my house - a totally different wiring system feeding a number of (mainly red) sockets all over the house (including by the CH control system, which is fed via a 13A plug) and also a series of 'permanently on'(when genny is on) lights at strategic points all over the house. In the event of need, all of that, but nothing else, is fed by the genny.You would do better to have a parallel independent system in your home for use on the rare occasions when there is a power cut. People with a standby generator often have a red socket next to the boiler so their heating system can be plugged in.
However, in relation to erics comments and my responses, there is no practical way in which I could avoid the genny's 'earth' being connected to the DNO's one (if I had TN,, which I don't).
Kind Regards, John