Depending on the source impedance (the impedance of the circuit coming in to the area), there will be more or less 'flicker' caused by high inrush currents. This is a fairly easy calculation given the cable size and length from the transformer and similar information on the circuit feeding the AC unit. It is based on Locked Rotor Amps for the AC unit. At my house, lights visibly dim when the AC system kicks in but it's rather larger unit than a small window cooler. Nothing gets damaged by this momentary drop in voltage. In every environment, 'flicker' is an issue to some extent. Even in large industrial establishments, starting large motors, even using Y-Delta starters, causes some amount of flicker.
Once again, I think you're looking in the wrong place. If it was a problem, it would be a problem for everybody's product. It's your product that fails. You can hardly expect your customers to leave their AC off in order to guarantee survival of a garden light.
A better place to look might be for some reference material related to electrical design for survivability in residential environments. Something that spells out what you need to design for. Then you need to build a test setup that will cause those conditions and test your product.
As to the article touting capacitors, remember that it is written by a capacitor company. Of course their product will solve all the problems of the world!