I want to assume you're referring to a website where visitors can simply search for applications or softwares to download. So yes, you can definitely apply for AdSense. AdSense program is intended for sites with the capabilities of drawing certain high amounts of traffic.
A software download site in my opinion has the potential of drawing more traffic than most websites or blogs. More visitors means more clicks and views, that also means more business for Google. Take softonic for example, the site is a complete download base site, you can find different forms of AdSense product on all pages of the site. If a download site violates any terms and conditions of AdSense policies, then sites like softonic wouldn't feature AdSense products.
By the way, there's also an alternative to the actual AdSense programs offered by Google itself for website or blogs who do not meet minimum AdSense requirements. It's kind of a YouTube program where you can opt to subscribe and have video boxes showing ads positioned anywhere on your site. You also earn on it just like AdSense.