Yes, if it is a payment plan that you set up with them, they can do it. On the flipside if you didn't pay the bill, then they could get attorneys fees and costs for collecting a judgment against you, which would likely be much higher than the interest that they are going to charge you. You can ask them what the annual percentage rate is for the interest amount and see if it would be better to borrow the money or to just use the hospital payment plan.
Attorney Haupt gave some great advice. It makes a lot of sense to look into how much interest the hospital wants to charge you. Anyone who charges you interest is required to disclose all the terms and conditions of the credit agreement between you. If they have not, you should request this documentation right away.
If there's anyway you can pay the $58/month (or better yet, the $100/month), it's really in your best interest to do so. If they send the bill to collections, the cost to your credit will likely be more than the interest they are charging.