Purpose of participating in "student doctoral programs" in conferences
In my field these are usually called doctoral symposia or graduate consortia. They are a great way to get feedback on your research direction.

They are generally setup as a discussion between a panel of professors and the other students that are participating. The students have an opportunity to present their research and receive feedback from everyone. This is nice because you also get to see other students in various stages of their PhD talk about their work and the feedback they receive.


  Also I was wondering if it makes sense to apply for one, considering I am already submitting a paper there


That is the best scenario to participate! You'll get to present your conference paper and get feedback from the doctoral program. Two birds, one stone!

Additionally, it is something you can put on your CV, the paper might be published in the proceedings depending on the conference, a great way to network with other students and professors, and some of these programs provide travel funding.

I'm currently working on applying to my second graduate consortium (this time as a mentor) and am really looking forward to it! The one I attended previously helped me a lot.