The short answer is no, you cannot. You need, as Stefan points out above, to purchase the corresponding Server license in order to see your QlikView documents. The QlikView iOS App works with existing, licensed QlikView servers. Apart from that, you can use the QlikView WebServer or IIS, it will work just fine.
The iOS app is free to download, and there is the demo site with many working applications you can use to check whether or not QlikView works as you expected.
Contact your QlikView sales rep in order to make him show you how server works, and answer your questions more accurately to fit your needs. In all cases, there is no such thing as "Personal Edition" for QlikView Server, other than the above.