No, collections agencies won't tell the credit reporting agencies to delete a legitimately late or delinquent payment. They might lie and say that, but if it is a legitimate debt, the most they will do is to indicate that the charge was paid in full, and when.
A medical bill for an amount of approximately $100 CAN affect your credit score, for purposes of getting a credit card. I know this because I had a similar situation to you-- I moved across the country and never received that piece of forwarded mail containing my doctor's bill co-pay.
I only found out about it because I was declined after applying for a new credit card. By then, the bill was 5 months late, so that it showed as seriously delinquent (over 90 days) on my credit report (FICO/Experian) and had been referred to a collections agency. I had no other late bill payments, my other credit card was current and had a record of 5 years of on time payment, no public record entries, and I had bought a car with a GMAC loan (no co-signer) and paid it off in full, no late payments.
I promptly contacted the collections agency, and paid the $80.00 debt. I asked if the record of it could be removed from my credit report. The collections agency told me that they would record it as paid in full. However, it was true that I had had a bill that was 90+ days overdue and had been referred to collections, so they would not remove it.
Next, I contacted the original physician who had issued the bill; they couldn't help.
Next, I contacted Equifax, Experian et al (the credit reporting agencies). They told me they would not remove the record of late payment, because it was true, but I could make a consumer statement explaining what happened. This would be attached to my credit report. I did that.
I applied for a credit card about a year later. I was denied again, due to having had a seriously delinquent past account, that same $80, even though I had paid it in full, and had provided an explanation regarding the circumstances. It will take between five and seven years for that bill to drop off your credit report, once you have paid it.
Different criteria are used for secured borrowing such as a mortgage or auto loan. If paid, your medical bill probably won't have any negative impact on your ability to get a mortgage in a few years, as that is collateralized by the house. Regardless, pay the medical bill now, get a receipt and a full statement from the collections agency that the bill has been paid IN FULL.