Can you test an app before you buy it on the iPad?
Sometimes app developers will release a version that allows you to play with it, but to get full functionality you need an in-app purchase.  See this app for Summoner Wars as an example:  https://itunes.apple.com/us/app/summoner-wars/id493752948?mt=8

But this is a choice the developer makes, so if the app you're interested in doesn't supply something like this (or a lite version; see @Alex's answer), then no.