There is no way to answer your question in the abstract. Any answer will clearly depend on the meaning of any particular criminal prohibition.
For example, if the prohibition were: "no person may hold data, in any form, knowing that it is [illegal, or whatever characteristic you mean to ask about]," then it would be likely be that holding data with knowledge of the data's illegality makes out the offence.
Even if the prohibition were phrased using the word "possess," interpretation of that single word in isolation would be an error of statutory interpretation.
canada
But for a specific instance, Canada's Criminal Code, s. 163.1(4) says:
Every person1 who possesses any child pornography is guilty of [an offence] ...
The Criminal Code specifically defines possession at s. 4(3). A portion of that definition includes:
For the purposes of this Act, ... a person has anything in possession when he has it in his personal possession
This has been interpreted by courts to require only: "actual physical custody of the object" and "knowledge of the nature of the object while with custody." For the Criminal Code, possession merely requires knowledge and custody.
Therefore, the offence of "possessing" child pornography does not require the ability to access that pornography. Accessing is a different offence. The "object" that is possessed is the "underlying data file," not a particular subsequent representation of it. This was explained by the Supreme Court of Canada in R. v. Morelli, 2010 SCC 8, paras. 25-28.
1. Note the definition of person in the Criminal Code includes a "body corporate, society, company, firm, partnership." But they are subject to the same mens rea requirement on the part of their directing mind. Just as for any other person, mere custody is not enough to make out this offence.