No, RS'ing an ineligible isn't an option.
There is some conjecture that putting more recruiting effort in may increase the odds of the player showing up. I've seen this tested with mixed results, at best.
Also, there seems to be somewhat of a correlation between how good the player is and how good your school is (i.e. a 4-star ineligible may be more likely to show up at Michigan State then at Eastern Michigan).