Hum... I think will not make any difference. The backgound stain is mostly due to the enzymatic activity in the tissue. If your peroxidase or alkaline phosphatase blocking steps are ok, it will result in less background.
However, this enzymatic activity is not completely blocked in some tissues like blood, or damage tissues in immunological responses like immune rejection.
Also, make sure your unespecific blocking step is working, this is also contribute for a good image in IHC, and be careful with DAB or the reagent you are using to precipitated.