I don't have such a combination, but if I read it right, the generator is able to make 2600W continuously and 2900W peak; that's about 21 amp continuous and 24 amps peak @ 120 vac. If the voltage is lower the current (amps) will be higher.
Converting watts to amps: Watts / Volts = Amps or properly stated P / E = I
The new Briskaire II 15K draws about 11 amps run (some web sites show 16 amps for some 15K units) and about 21 amps to start, which could be lower with the start assist capacitor, such as the Supco SPP6.
By the numbers along and only running the A/C on the genset, it should be able to do it. I would think the 3000W (actually 2600W) Dometic is undersize for daily and / or continuous use.
BTW, Dometic recommends a minimum of 3500W genset for both the 13.5K and the 15K units.
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