question

No.

As you say, the 5k is rated 4000W continuous at 25°C, so a 4500W load for an hour or two to heat water won't work.

You'll also need more than a single 100Ah battery, as it'll only last for just over an hour pulling close to 1C, so not an ideal setup.

Get yourself a 3000W immersion element instead and you'll have a better chance of making it work.

@JeromeP The MP-II 8kVA 6400W would be another option to keep things easy and simple compared to a parallel setup. It may be worth stretching the budget.

It might as a single load. Water heater loads are resistive, not inductive, so you can work from the VA figure. And then you have an excess of 500VA. Question with that is how long before it de-rates the output due to heat in the Multiplus.

What may also help is reducing the output voltage. Grid voltage is nominal and as long as you stay within normal range, everything will work safely but the heater will draw less current. E.g. in England voltage is nominally 240V. Electrical kit runs fine at 220V. Same will apply running a 120V nominal at 110V. That's close to a 10% voltage and power reduction.

Would using the Power Assist on the Multipus II be of any benefit to bring the ac output wattage up to 4500 while on the 3500 watt gas generator?

@JeromeP I've run my MPII 5kva unit flat out for 2 hours. I managed to maintain about 4.4kW for about an hour before it started dropping to 4kW, then by the end of the 2 hours I was down to 3.6kW. That was with a power factor of about 0.9. When I added 3No small fans to the top of the MPII unit, I was able to maintain over 4kW for the whole 2 hour period.

That's quite impressive, a bit taxing on the unit. Was this done without Power Assist if applicable?

Thanks. That would be a good option for the water heater but I don't want to risk lowering the ac limit, there is a good chance I may forget to set it up again to 120 volts to run my electronics, unless I'm missing something here.