Synchronous Generators: Full load and No load
Of course you can connect a load that's larger than full load.

The data sheet tells you what happens at full load. Unfortunately, the data sheet probably doesn't tell you what happens at more than full load. You would have have to do the experiment to see whether it failed to self-excite into it, exploded, blew a fuse, tried then shut down safely, or how long it took to overheat.

There is a school of hobby engineering that assesses maximum ratings by ignoring the data sheet and turning it up until it explodes, then backing off a bit. Sounds like you adhere to this teaching. Professional engineers tend to stick to the data sheet. Often the manufacturer has spotted something in the months or years of development and qualification that the user hasn't yet.