Yes it possible to do a course while on Illness Benefit but not advisable. Perhaps you have some reason for not wanting to involve SW but I have always found the only way to deal with them is be straight and ask them to advise you on the options available to you.
I done a night course on illness benefit this year and sw where fine with it actually they where fantastic and gave me some help towards to fees, might you it was only one night per week the best of luck