In short, yes.
But with some qualifiers attached. “Low” is a relative term and although lenders do rely on credit scores during the approval process they’re not the only factor. Important, yes, but exclusively so not necessarily. It depends upon the type of loan you’re applying for.
Credit scores range from as low as 300 to as high as 850 although any mortgage lender will tell you they’ve never encountered a loan with either a 300 or an 850 score. There are three credit repositories, Experian, Equifax and TransUnion and they all use the same algorithm to come up with a score. There will typically be slight variances within the three reported scores due to when and where the credit information was reported to each of the three. Lenders will use the middle score, ignoring the lowest and highest.
Most lenders will ask for a minimum credit score of 620 but some loan programs allow for a score as low as 580. Not every lender will approve a loan with a 580 score but some do. There are also special circumstances that can explain a very low score, such as something closer to 520 but it’s up to the individual lender to make the decision whether or not to approve a loan. Typically the lender would rather wait until the borrowers have repaired their credit to the point where scores approach the 620 number.
Borrowers may also be eligible for an FHA loan with low scores. Typically the borrowers need to document why their scores are so low and provide evidence the event that caused the low scores was a one-time affair and the event was beyond the borrower’s control. For those who do wish to get a mortgage with a low credit score they need to be prepared to accept higher interest rates with an eye toward refinancing in the future to get a better rate.