Consult with the factory but I don't see any reason it wouldn't work. The electronics will have a power supply flexible enough to handle voltage 15% lower than expected. Sizing could be a deal-killer, though.
Should be fine for tea
According to my math, the SR15L-277 will draw 13A (12.996A) on 240V. That will give it an effective power of 3120 watts.
The SR20L-277 will draw 17.32 amps at 240V and provide 4156 watts.
What concerns me here, however, is - if I was off-grid, with a 5000W inverter for my whole house, I wouldn't be prioritizing an auxiliary kitchen spigot for hot water for tea. Which worries me that you're trying to use this thing for your whole-house hot water supply, for everything from showers to dish washing. That's going to miss by an order of magnitude. Let's compare.
A British electric shower (with a notably low flow by American standards) draws 8500W, 9500W or 10,500W depending on model. My own rule of thumb is 40A (9600W) per GPM of flow you want. So your 13A setup is going to provide 1/3 GPM or 12 seconds to fill a teacup.
As you can see, the numbers just aren't working for bathing or washing dishes. You're off by an order of magnitude. Sizing errors are the classic blunder with tankless heaters. So many projects fail (with much more power than yours) because the designer thought they could scrimp on capacity to squeeze it into an available electric service.
Don't use batteries for large-scale resistive heating
Since you're coming off an inverter, you're coming off batteries, which are still pretty precious at >10 cents a watt-hour. And that problably came from a constrained source such as solar.
Outside of momentary uses like toasters, microwaves or induction stoves, it is absolute madness to trade away such precious power for heat at only 3.4 BTUs per watt-hour. That rather tepid 34,000 BTU British electric shower, you have to rack 1000 watt-hours of battery to run that thing for Six Minutes. That's a whole Group 27 battery or three Nissan Leaf v1 modules.
You need a physics cheat code: heat pumps. Heat pump water heaters are now standard products at sane prices. They chill the room they're in, so some clever ducting of that space might be useful (either to capture the useful air conditioning, or vent unwanted cold). They are tanked heaters, so they'll need some space and some weight (30 gallons = 250 pounds of water).