Answer:
In a word, no. The Fair Credit Reporting Act provides that you have a permissible purpose to obtain the report, and you do not need permission from a consumer asking to open an account.
Many financial institutions users post signs in their New Accounts area saying that they use ChexSystems (or another service provder) when opening accounts. That's not a requirement; it's thought that the signs help to discourage new account requests from people who know they have a poor record for maintaining accounts.