It's been done on very small scale tests like the SCOPEx test. It's done with marine cloud brightening (MCB) which is a different thing.

However, SAI is absolutely dangerous and if it's not continued indefinitely it will lead to termination shock. Because all of the CO2 emissions remain and will even increase, if you suddenly let that sun energy in again, all of the bad climate change effects will happen in months to several years, instead of many decades like it would normally. That would absolutely lead to war, billions dead, most agriculture dead, and near a complete collapse of the entire biosphere.