The answer to the OP's question depends on three main factors:
Altitude.
The amperage rating on the generator.
The locked rotor amps coming from the A/C.
There are other factors as well, such as generator fuel quality (I've found Chevron Premium + Star-Tron quite effective), and length of the power cord.
2500 watts for a 13.5k BTU A/C is iffish. An Onan 2800 watt model can start a 13.5k BTU A/C with 300 watts to spare (as per Onan's documentation.) An Onan 2500QG can start a 13.5k BTU A/C with 0 watts to spare. So, officially, Onans can do the job.
Does it mean a 2500 peak generator fresh off the boat from China made as cheap as possible have the ability to do this? There are a lot of fudge factors such as measuring load capacity in volt-amps, or finding that the constant load is a few hundred watts than what the item is rated for. Combine this with a tendency for no-name Chinese over-ratings of generators (saying an ET800 rattletrap can handle 1000 watts, for example), and unless the maker puts out specs similar to Onan's, nobody here on rv.net will know. They won't know on irv, or any other forum, almost certainly.
Without the manufacture's statements, the only way you can know for sure is to take the generator and A/C, attach an oscilloscope and other tools, and get measurements of the generator's output under load, temperatures on the compressor, and other measurements by expensive, specialized equipment, and find out by oneself. However, can one save a log of a generator's exact phase changes from when it starts to the A/C clicking on, to power down, and looking for bad sine waves and voltage surges/spikes? Not many people have these instruments to do this.
As a rule of thumb with a 2500 watt A/C and a 13.5k BTU A/C, not knowing how high in elevation the OP is... I'd say no just to be safe, so the OP doesn't wind up burning out both his generator and his A/C compressor.
Yes, I can point to people happily running 13.5k A/Cs from a 2500 watt Yamaha unit or even a 2000 watt Honda... but anecdotes don't help much... either measurements from an oscilloscope and other meters on the test bench or hard numbers from generator and A/C makers are the only thing one should go on if one is in doubt, and forums show that there are mixed results.
If in doubt, buy a notch bigger in generator, or see about pairing... and the generator the OP mentioned cannot be paired.
