Is there a way to browse the OS X App Store from iPad?
As @jaume has mentioned, you can use the Mac App Store Preview on Apple's Website to browser apps from the Mac App Store. The same exists for iOS apps and is labeled as iTunes Preview.

As you will have already noticed, the search box on Apple's website is not very helpful when searching for Apps. The best alternative I can think of uses a google query. In the Google search box type:

site:https://itunes.apple.com/us/app/ "Mac App Store" MyKeyword

...which uses the URL:

http://www.google.com/search?&amp;q=site:https://itunes.apple.com/us/app/%20%22Mac%20App%20Store%22%20



Copy and paste the URL
Add your keyword to the end (separate multiple keywords by %20)