I think it's important to note that the USN never anticipated sending battleships out beyond the Hawaiian islands for the first year or so of any hypothetical war against the Japanese. The Battle Force vs Scout Force Fleet Problems had demonstrated several times how dangerous carriers could be to battleships without air cover. Without carrier air cover, the battleships probably wouldn't go beyond the range of land-based aircraft from bases in the Hawaiian Islands.
True and not true. War Plan Orange called for two BB to go to Samoa for 3-6 months as soon as the war started to keep the lines open to the Aussies. So it is probably better to say that we did not plan to operate on a consistent basis within the range of Japanese air cover. It is also important to note that we greatly underestimated the range of Japanese planes.
We had plans for battles in the Marshall Islands and at Truk. It is just that we had just enough fuel to get to Truk, fight for a day or two, and get back on fumes. So no one really thought about these too seriously once the war started. It is also a little appreciated fact that the loss of the BB freed up enough fuel reserves to allow the carriers to be very aggressive early in the war.
And you can get an interesting insight here. Moving the fleet to Pearl was strictly diplomatic move since we were moving it from a well supplied base to what in many ways was still a base under construction when one thinks of logistics/supplies. We might well have had better fleet range if we fuel everything in San Diego, sent the fleet to Pearl for quick top off. The tankers could likewise fuel up in San Diego and top off in Pearl.
So what happens if the carriers die but the BB live. Like all things, it depends a lot on the POD. The BB out at sea is different from BB at San Diego is different from the BB being luckier and better air defense. But let's take the easiest POD that is closest to the date. The USA gets a few hours warning, and gets the fleet formed up to fight. The Japanese do the initial attack on Pearl air defenses and port, but it is mostly empty. Later that morning, Japanese air and USA air engage. We lose both carriers (two were in region if memory serves me). Have Japan lose two carriers too as Japan expected. Japan air crew losses will be much higher than OTL. The initial raid will be worse since our fighters will be up and the AAA is manned. We then have Japanese losses on second strike which is over the ocean. Japanese losses on CAP on USA strike, plus more crew losses when two CV go down. Say Japan leaves the day with less than two full CV aircrews. Or three if you like. Here we have the nice scenario in the thread of the the CV being gone and the BB reputation being intact.
What happens? We get a rescue mission to Wake Island. My guess is 4 BB with 2 BB being prepped for move to Samoa, two BB damage in port. Probably successful since Japan is roughly at half OTL aircrew strength an 2/3 CV hull strength. We see aggressive BB action up the Solomon Islands if Japan still comes down fast. We have put a crimp in the Japanese war Plans, so their time table may be off. We lack the land forces to attack the Marshall Islands. If the Pow and Repulse still die the same way (not a given), then we will know to stay away from Japanese land base air. So we may well keep the 6 BB Pearl, 2 BB SW pacific force structure. As BB are damage or sunk in or around Australia, we may well send replacements.