You have mentioned that the data are stored in mysql. You are going to write a java program that will retrieve/manipulate the data. One reason for why you can use application server is to take advantage of some of the features of applications server such as connection pooling.
Of course you can implement connection pooling of your own but it consumes time.
If you use CMP feature, then it can help you in reducing the development time.
But in my opinion the most important feature of any application server is scalabity in terms of number of users connected concurrently. If in your application the requirement of scalability is too high then I would suggest you to go for application server.
I think one of the best advantages of using an App Server like JBoss is the J2EE CMP functionality. Once you understand how CMP works, it cuts out the data access layer you would normally write in business apps as SQL code can get quite involved at the best of times.