Having the Olympics and Paralympics at a different time is like having a totally different Olympics for people of a different color or a different gender, they're still humans participating in sport, It's socially wrong. It would not be counter productive whatsoever, it's more so counter productive and less economically wise having them at separate times and in different places. Though it may not be a broken system, nor would it be if they were put into the Olympics, people that participate in the Paralympics are much more stars than any other sports performer.
The Olympics themselves are filled with individuals who do the best with what they have, genetically. The fact is most of us, no matter how much we trained, could never reach the level of ability possessed by Olympic athletes because we are physically unable. So why not have games for those who are not among the elite, but still do the best with their physical limitations. We have games for the elite, such as pro sports and the Olympics, and a myriad of championships for average people such as local, state, national and international amateur competitions. Why not allow the same, and allow the same showcase, for those overcoming a major obstacle?
Yes, the special and paralympics should be held in conjunction with the regular games. Those less fourunate deserve equal treatment, if not more for their amazingly difficult efforts to compete. Disabled people should be allowed to share the spotlight with others.
The Olympics already draw in a massive amount of money and people to whatever site they have it in. Special Olympics are typically held in smaller communities. They don't have to go on at the same time. It would be counter-productive. Keep the Special Olympics and the Olympics doing what they already do. It isn't a broken system, so we shouldn't try to fix it.