It's all up to the renter. They may not even check unless they have a property manager doing the leasing. They will check. So, yes, it most certainly can and all things being equal, the renters will rent to someone reliable who they know will pay because the lass thing they want to get involved in is an eviction. Your chances are much better if there's no property manager.
That's the short term. Long term, you need to fix your credit so you can stop throwing away money and buy a home. Now is the time as interest rates are really low. If Congress doesn't get their act together, it's going to be bad news for all interest rates and buyers. So act soon.
Best of Luck,