Biochemistry textbooks generally tell us that we can't turn fatty acids into glucose. For example, on page 634 of the 2006 and 2008 editions of Biochemistry by Berg, Tymoczko, and Stryer, we find the following: Animals Cannot Convert Fatty Acids to Glucose
If acetone can be converted to acetol, then it can also be converted by the same method to another useful substrate, dihydroxyacetone, which would become phosphorylated.
2 Acetyl-CoA -> BHB -> Acetoacetate -> acetone + CO2
If acetone can be converted to acetol, then it can also be converted by the same method to another useful substrate, dihydroxyacetone, which would become phosphorylated.