Keeping a balance hurts the 'credit utilization' portion of your credit score. You're using a higher percentage of the credit allocated on that card(s).
So what? Even if your CS goes down a bit, you're gaining a 0% loan. (beware of 3% fee or so on some cards to start)
In my experience, the lowering effect fades pretty quickly. The score starts to creep back up.
Try to keep the other components of the CS as high as you can:
Credit utilization: 35%
Payment history: 35%
Length of history: 15%
Types of credit: 10%
Credit pulls: 10%
A business card is not included in the utilization portion of the score, so using the Ink or other business card for the free loan won't affect your score at all.