Yes. No policy governs in-breeding or line-breeding. That said, if the breeding was accidental, the breeder is advised to registering the pups with non-breeding status.
Can in-bred pups be registered?
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as of Nov 2020
State/Prov. Amount Alberta $ 930 Alaska $ 378 Alabama $3,172 Arkansas $1,676 Arizona $1,886 British Columbia $ 317 California $2,399 Colorado $1,578 Connecticut $ 815 Dist. of Columbia $ 2 Delaware $ 92 Florida $1,597 Georgia $1,962 Hawaii $ 5 Iowa $2,069 Idaho $ 888 Illinois $ 992 Indiana $4,467 Kansas $4,173 Kentucky $ 844 Louisiana $4,801 Massachusetts $1,333 Manitoba $ 364 Maryland $ 476 Maine $1,558 Michigan $2,852 Minnesota $ 774 Missouri $1,658 Mississippi $1,250 Montana $1,312 New Brunswick $ 95 North Carolina $1,839 North Dakota $ 635 Nebraska $1,974 New Hampshire $1,014 New Jersey $1,756 New Mexico $1,153 Nova Scotia $ 28 Nevada $1,193 New York $ 748 Ohio $5,216 Oklahoma $1,933 Ontario $1,331 Oregon $2,508 Pennsylvania $4,340 Puerto Rico $ 38 Quebec $1,223 Rhode Island $ 205 South Carolina $2,048 South Dakota $ 225 Saskatchewan $ 646 Tennessee $1,971 Texas $6,085 Utah $ 944 Virginia $2,558 Vermont $ 463 Washington $1,868 Wisconsin $ 999 West Virginia $2,644 Wyoming $1,022