Short answer is that when the grid connect solar system tries to export into the "grid" you've established with a petrol powered machine, the generator will be burnt out, possibly along with your house appliances, if the inverter works at all.
As a broad rule of thumb, solar systems and generators do not play well together. Either the solar system wont synchronise or the generator will be burnt out, but I'll try to explain further.
An ordinary grid connect solar system, and grid hybrid batteries for that matter, are what they call a grid following device. It looks at the voltage and frequency coming in from the street and takes a statutory one minute to make sure it's stable before coupling up and synchronising it's output. The grid is an infinite tank or buffer that will forever soak up any excess, so it's easy to work with.
If you want to run a generator, which to be honest can be a little unstable, then what you need is an "off grid" inverter that is capable of grid forming. That is they're able accept a non-sychronous input or they can shift voltage and frequency output to match a somewhat variable generator. Victron, SMA, Schneider make good units but I can't recommend a Selectronic SpPro highly enough.
In an off grid system, your own batteries are the tank or buffer into which you can pour energy, but when they're full it's trickier to keep everything happy. You have to be able to exercise much finer control of both the solar and the generator
Some hybrid battery systems rely on the grid for stability and even if you have sunshine available they still do not charge from solar. Other grid hybrids will operate as a "stand alone" system but they're generally a limited capacity and aren't actually designed for continuous service. They can get you through an outage but they don't offer a warranty if you run without the grid available for more than perhaps 20% of the time.
You can run your house on a generator, it's perfectly acceptable and most electricians are able to install a changeover switch to do just that. However your house would be petrol powered, the solar system would be connected to the grid side of the switch to make sure that it doesn't try to "export" back into the generator when there's lots of sun and no energy being used.
Unless the generator is a pretty healthy sized machine, (ie 3 cylinder diesel, 15kVa or more) your electrician should also segregate the switchboard into essential and non essential loads. This is a common approach with solar battery hybrid systems as well, they generally have a limited capacity.
What it boils down to is budget versus utility. If you need a bulletproof system to run the whole house and keep a computer server online totally uninterrupted then be prepared to spend $30k(?) on an Australian made SpPro with batteries and solar. They'll do some energy management as well.
If it's just that you want a reliable power supply to maintain a freezer full of food or aquarium full of fish, and it needs to be automatic in case you're not home, then a grid hybrid solar system with batteries is a great way to minimise your bills and have some backup capacity. Just make sure it's not too cheap. Many of the budget options have disappointingly small surge capacity, they struggle start the fridge as well as run the lights.
If you just want a manually operated emergency supply, then a socket and switch can be fitted fairly cheaply to the switchboard. You could use the camping generator you already own. Or a bigger generator can be hard wired and arranged to auto start, but they will never be able to save you money every day like solar can.
Lastly, you can have a V2L system where an onboard inverter in your EV will use the mammoth EV battery to power external loads, like a camping generator does. However there have been problems reported with some EVs having sensitive RCD/earth leakage devices which do not play well with the MEN in your house switchboard if the house has been wired for a temporary generator input.