In the end it would be up to the lender as to if they would make you pay it. A lot would depend on the amount as well as the type of debt. If it was for something like a medical bill they may not, but if it is for a credit card debt they may require you to pay it off. Their biggest fear from them is if you get sued would you then have to default on the mortgage, basically making you a higher risk.
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It is standard practice for lenders to require you to pay off collections before granting a mortgage loan. This is potential debt that may come back to haunt you and interfere with you making your mortgage payment or a lien against the property.
A low credit score will automatically exclude you for consideration by some banks but that isn't the only factor. If you have a good score it may be worth the lenders time to look at your application and credit history. If these are fine, the bank will consider the value of the property, the loan amount, the down payment, stability of your employment and your ability to repay the loan.
I have never known anyone to get approved for a loan based on credit score alone.
It really depends on the lender.
Back about 5-years ago when my Wife and I bought our home I had a small collection on my credit from a apartment complex and after I explained that a six month lease was actually a 7 month lease and that I had 6 concealed checks to prove I had paid they said not to worry about it.
But it was only $265.00 so it was really no big deal to begin with.
Most lenders require that unpaid collections be paid because if they go to court and get a judgment a lien can be placed on the property. In my case there was no way they were going to take me to court over $265.00, so it really comes down to the risk factor for the lender.
Score alone will not get anyone approved it comes down to a combination of score and profile that matters.
It is the contents of your credit report that determines your credit score.
So the contents are more important then the score.
Things like late payments, accounts in collections, charged off accounts and judgments are a killer of ones credit score.
As to a mortgage, they will want those unpaid collection accounts taken care of as that could lead to a judgment and a lien placed on the house.
Hope this helps answer your question.