Can a corporation really adopt a person?

I'll interpret your question to specifically relate to US adoption laws, as you are referring to the case in the Truman Show.

I am not a legal expert - but I've briefly reviewed "Corporate personhood" (from Wikipedia) and "Who May Adopt, Be Adopted, or Place a Child for Adoption?" (pdf from childwelfare.gov).

I think in short the answer is no - under current laws a corporation could not adopt.

It appears that in general State adoption laws indicate that single adults or a husband and wife are generally required to be adopted parent (I know that in Michigan this is being challenged by a same sex couple who would like to be able to jointly adopt - but this does not challenge the premise of my answer). The state laws indicate minimum ages for adoptive parents and/or a minimum age gap between the new parent and adopted child. Corporations do not have 'age', and they are not generally referred to as adults.

Corporations are treated as people in some aspects of the law - this goes back to the constitution, both as corporations are groups of people and should be afforded protections as such, but also for convenience to treat corporations as entities. As a result they can enter into contracts, make political donations, be taxed or sue and be sued in the courts. However the courts have often restricted the rights of corporations and they do not have equal rights to citizens - e.g. a corporation has no right against self incrimination as a person does under the Fifth Amendment.

It seems to me that the rights of corporate personhood are resticted and current state laws would prevent adoption of a child by a corporation.

Adoption requires close scrutinizing of the prospective environment and guardians. They don't just allow anyone to adopt, and it is inconceivable that an entity (such as a corporation is) could actually adopt a child. The movie was purely satire about the voyeuristic nature of our current entertainment choices (particularly "Reality TV" shows).