Can a collection agency for a non-credit card-type bill hurt your credit rating?

Yes

Once a collection account is reported to your credit history, its origin no longer matters. If money is owed and it gets listed with a credit reporting agency as a collection account, it affects the main factor in your credit score: Payment history.

See www.myfico.com/CreditEducation/WhatsInYourScore.aspx for details of a FICO score.