If might take anywhere from 9 to 12 months to strip her down and put in new equipment, wiring, power plants, comm lines that also might take anywhere from 6 to 9 months and then go to sea trials that might make her available by late 1943 early 1944??
Even if this wildly optimistic assessment was the case, that would have her commissioning alongside the Iowa's. If the US wanted another battleship for that time frame, they'd just build a fifth Iowa, or a Montana. The US didn't; BB65 and BB66 (planned Iowa class Illinois and Kentucky) along with the entire Montana class (those never got their keels laid) were canceled. The four OTL Iowa's were mainly completed because they were fast enough to escort the fleet carriers. Bismark was three knots slower.
The USN entered the 1940's with 15 battleships. Two more were commissioned before the war, and eight during it, all by the end of 1944.
The IJN never had more than 12 battleships and battlecruisers combined, and the German navy was more than countered by the RN.
The USN didn't need any more battleships for 1943-1944.