you will probably never get service or parts on this unit - hope it never breaks. Also, they would never stock or sell you parts directly here or through your European intermediary

If you are buying Gaggenau you better verify with them directly. With equipment in this price range you don’t want to make any mistake.

We're in a tough spot, narrow counters so we can't do a downdraft behind the cooktop, and the counter backs up to windows so we can't do an overhead:/

There is one downdraft induction cooktop sold in the US: Elica ENT432BL. The opportunity for a Tesla in the kitchen! Well, Nikola Tesla.

In general, going from international markets to the US is more likely to work than the other way round. There are a couple of subtle differences.

European appliances are nominally rated for 230V. But that's a convenient lie. European power grids don't actually provide 230V. They either supply 240V (in the UK) or 220V (everywhere else). When the EU decided to harmonize grid voltages, they did this by extending the acceptable under-/overvoltages that appliances have to accept.

So, while a Gaggenau range would expect to get 220V in Germany, it must accept up to 240V, if sold in the EU. And conveniently, 240V is exactly what you'd wire it for in the US.

The next difference is that Europe usually wires residential homes for three-phase power, whereas the US uses split-phase systems (unless this is a large apartment complex or a commercial building, where you'd again see three phases).

This means that you could find European appliances that require 400V three-phase power, and there really isn't any practical way how you'd install those in the US. Fortunately, that doesn't appear to be the case with this Gaggenau product. You could also run into a situation where your apartment only gave you access to either 120V or 208V. That would also not be supported. But you'd likely know if your house was on three-phase 120/208V service.

The next difference is that in the US, a split-phase system provides you with both one (or two) hot legs and a neutral leg. There are some US appliances that require this neutral leg. On the other hand, in Europe you don't have polarized plugs, and you don't get the center tap. One of your 240V legs has 0V potential relative to ground, though (similar to how the neutral in an American 120V circuit works). Due to the lack of polarized plugs, this difference would only matter for hard-wired appliances; but even then, I have never seen a European appliance that required the 0V potential between neutral and ground. So, you are almost always guaranteed to be fine powering a European 230V appliance from and American 240V power source.

Finally, the big difference is line frequency. 50Hz in Europe vs 60Hz in the US. In practice this really only matters for two things. Synchronous motors run about 20% faster when brought from Europe to the US and can overheat. And all transformers and switching power supplies produce about 20% less waste heat than in Europe. As you are not dealing with a motor and as the entire appliance uses solid state circuitry to regulate power, none of that matters much. And in fact, it is not surprising that the data sheet lists both 50Hz and 60Hz as acceptable input frequencies.

So, yes, both common sense and an inspection of the data sheet suggests that there is no technical reason why this appliance wouldn't work when connected to both phases of an American mains power supply.

Your problems are more likely to be logistical (see earlier comments) and possibly regulatory. You might want to check with your home insurance if they object to you installing this type of appliance, as it is unlikely to be UL listed (even if the equivalent CE testing is likely as least as strict).