That's the general idea, but the devil is very much in the details, as explained below the break.
Chapter 11 is a detailed set of statutory provisions that build on general Bankruptcy Code provisions and an enormous body of caselaw. Moreover, there is a large and experienced Chapter 11 bar, and specialized government representatives (United States Trustees) monitoring the integrity of the process, and bankruptcy judges overseeing, and to some degree managing, the process. This legal infrastructure has also created market confidence in the ability of the Chapter 11 process to fix struggling businesses. Not every business can be saved, but for those with a chance, Chapter 11 works pretty well, and investors are willing to invest in the reorganization process (through bankruptcy claims trading and DIP financing and exit financing).
That rich legal fabric of law, institutions, and personnel, and hence market confidence, is missing from a potential Fannie/Freddie conservatorship. There only thing to guide a GSE conservatorship (beyond general conservatorship law and principles, which may or may not be applicable) is a fairly barebones section of the US Code, 12 U.S.C. section 4620. It gives the conservator (which could be pretty much anyone, including a government agency) some avoiding powers (although more limited than a trustee in bankruptcy), prevents the operation of ipso facto clauses against the GSE in conservatorship, and creates a possibility (but not a requirement) of a 45 day stay of actions against the GSE. The 45 day stay is the real key because it provides a window for a workout to occur. But is it sufficient?
The 45 day stay contrasts to the bankruptcy automatic stay, which continues until the end of the case unless lifted for cause. The 45 day stay appears to be modeled upon the stay for FDIC conservatorships, 12 U.S.C. 1821(d)(12). But the FDIC is in the business of doing bank conservatorships and receiverships--it is experienced and set up for handling failed banks. OFHEO, Fannie and Freddie's regulator, is not, and the FDIC is not really set up to handle a failed GSE. 45 days is a good stretch of time for the FDIC to resolve a failed bank, in part because the FDIC can strongarm other banks into taking on assets and investments of the failed bank. But 45 days might not be enough time for a Fannie or Freddie workout. There no OFHEO conservatorship team or experience in handling failed GSEs. And the conservatorship provisions do not permit DIP management (see 12 U.S.C. 4619(a)(4)(B)(i)). And the scale of Fannie and Freddie is alone an obstacle. To be sure, the Treasury Department would likely bring significant pressure to bear on parties to a workout, but that might not be sufficient (remember the Master Liquidity Enhancement Fund debacle last fall?).
It seems to me that if a Fannie/Freddie conservatorship were to be viable, the stay would have to be extended. On the other hand, if Fannie or Freddie went into conservatorship and couldn't reorganize within 45 days, it might be as good as dead. Regardless, a major problem with the GSE conservatorship option is that it doesn't have the infrastructure to work like a Chapter 11 reorganization. Although that arguably gives the conservator a freer hand, it also reduces market confidence in the ability of a conservatorship to set a faltering GSE back upright. And without faith in the ability of a GSE to reorganize, the reorganization is unlikely to succeed.