question

Because of the large 220v power requirements for these machines most people recommend a 20kw diesel generator.

Are you in the USA?
In the USA, the Grid is 240v / 120v Split-Phase or 120v / 208v 3-Phase WYE.

Will the ice cream machine (208v-230v Single Phase) operate correctly with 240v Single-Phase?
If they say "Yes", then I would get that in writing

6,500 watts (running) = 240v x 27 amps just for the Ice cream machine
I doubt, the Genmax GM10500iETC alone, can start your ice cream machine.
And it will consume ~1.5 Gallons gasoline per hour.

Do you have a local Victron Dealer that can help you?
You need a complete off-grid system design.
You need to know the surge amps and surge duration of all motors and/or compressors in your equipment.

Will you have any refrigeration equipment?

Also watch the machine ratings. 5kVA is about 4000W, depending on the load characteristics.

Yes, USA

The manual says supply voltage +/- 10% of that range.

I understand the generator alone is insufficient. My thought was the generator would be to replenish battery supply and be available for peak usage when needed.

I don't have a local Victron dealer but I understand this would be a complete system. I'm just trying to validate the feasibility and get an idea of what components would be needed.

Generally the Multiplus will add up to its max current to the input current. However some generators don't deliver clean power and this may reduce what you get.

This from the Easysolar II 5kVA manual (multiplus inside)

AC-out-1 The AC output cable can be connected directly to the terminal block 'AC-out'. From left to right: "N" (neutral), "PE" (earth) and "L" (phase) With its PowerAssist feature the Multi can add up to its rated power (e.g 3000 / 230 = 13A) to the output during periods of peak power requirement. Together with a maximum input current of 32A this means that the output can supply up to 32 + 13 = 45 A. An earth leakage circuit breaker and a fuse or circuit breaker rated to support the expected load must be included in series with the output, and cable cross-section must be sized accordingly.

You need real current figures for your equipment and size the electrics from there. Beware of inrush currents. Also beware of temperature derating. Ice cream for me means a hot environment and there's a good possibility of reduced output due to this.

Might also be worth considering ramp up time for generator and inverter to produce the necessary output.