You have no legal obligation to support children that are not biologically yours or yours by adoption.
So, the answer is no, at least not directly.
Indirectly, he may have a little more disposible income once you two are married. While two people cannot live more cheaply than one, two people living together can live more cheaply than two people living separately. However, I believe IL CS guidelines are very much a percentage of income of the noncustodial parent. They may allow for some variations based upon the whether he has covered them on his health insurance at his expense and maybe there is some variation based upon the number of nights that he has custody, but that usually about it with most of these child support guidelines unless there are multiple support orders.