The sun will be further north during most of the year. If the evap cooler is directly west of the panels and only casting a shadow late in the day during Summer then it won't really be an issue. But if it's north of the panels then that's certainly a big problem.
Since they are wired in series, and the panels themselves are also in series, shading part of the array disproportionately drops the output relative to the area shaded. So you want no shade at all if possible for most of the day.
The Evap is indeed West of the proposed area, and the only shade from 6am-9pm is from around 7pm where the shadow forms. If what you say is true about the sun being further north most of the year, this will alleviate that problem.
So in essense this isn't a deal breaker, just a reduction in effeciency for that part of the evening?