think you are stuck with trial and error. If it's a low enough watts to power the pump, i assume that's the only electrical components?, then it can. theer should be info on how many watts can be produced by teh solar panel and how much light to achieve it.
talking 10% of artificial light, not the sun, so you may have to set it up and see what happens with objects simulating larger in-bloom plants and position the panels.
you could take some light readings and contact the manufactuer.. say is 7klux enough to produce the watts needed to either charge the battery in time between uses or simply power the pump as is... don't need any experience to understand this. You won't have "strong" light missing the plant or along boundaries. a systeem that charges a battery might be better than one that does not.
if you are talking about using the grow lights specifically for this water system - definitely don't do that. lol, you'd have the inefficiency of the lights factored by inefficiency of the solar conversion and you'd spend 10x more on whatever you are doing, lol.