Thank you for using JustAnswer.
Per your questions:
Is it important to do so? - If he doubts that he might be the father, that would be a good idea. Otherwise it's probably not an issue that he should worry about.
Is he legally bond to support the child under Il law? - Assuming that the child is born in Illinois, yes. The Uniform Interstate Family Support Act (UIFSA) governs this, in that the state of residence law will govern child support and visitation. Every state makes it so that the biological parents have a duty to support the child until a court terminates such obligation, and they'll only do that if someone else is willing to take on that responsibility (i.e. adopt the child).
If he moves out of state for a job is he still leggaly bound to the child?- Yes. Moving does nothing to affect his obligations, although it could affect his rights (reduce the visitation that he has).
Hope that clears things up a bit. If you have any other questions, please let me know. If not, and you have not yet, please rate my answer AND press the "submit" button, if applicable. Please note that I don't get any credit for my answer unless and until you rate it a 3, 4, 5 (good or better). Thank you, ***** ***** luck to you!