Coasties would still be a part of the Department of Treasury, where they were until the Department of Homeland Security.
If that were the case you'd probably end up seeing the Navy win the fight in the late forties between them and the USAF over the future of the American military. The USAF was saying that they could win wars by themselves, just by nuking people. The USN said that that was ridiculous and wanted a large fleet of supercarriers. USAF won, but USN was right. Odds are that, although the USAAF would still have some large strategic bombers and fighters, they would (thanks to being tied to the Army) be a lot more focused on providing close air support. The Army would probably be at a higher level of training post-WWII and so there would have been usable Army units at the beginning of the Korean War. The Navy would have better funding since they'd still be Cabinet level. Jointness would have been at the same level it was in OTL, that is, non-existent until the 1980s.