Não, pelo menos não se o navegador for compatível com os padrões.
Por Mecanismo de Gerenciamento de Estado HTTP RFC 6265 , se o navegador oferecer a opção de desativar os cookies, selecionados pelo usuário, o navegador não deve incluir um cabeçalho do Cookie em Solicitações e deve ignorar a cabeçalho Set-Cookie em objetos de resposta.
Isso significa que não apenas um servidor não conseguirá definir um cookie, mesmo se o fizer, seu navegador não o disponibilizará ao fazer uma solicitação para um site no caminho dos cookies.
RFC 6265 HTTP State Management Mechanism April 2011
7.2. User Controls
User agents SHOULD provide users with a mechanism for managing the cookies stored in the cookie store. For example, a user agent might
let users delete all cookies received during a specified time period
or all the cookies related to a particular domain. In addition, many user agents include a user interface element that lets users examine
the cookies stored in their cookie store.User agents SHOULD provide users with a mechanism for disabling
cookies. When cookies are disabled, the user agent MUST NOT include
a Cookie header in outbound HTTP requests and the user agent MUST NOT process Set-Cookie headers in inbound HTTP responses.Some user agents provide users the option of preventing persistent storage of cookies across sessions. When configured thusly, user
agents MUST treat all received cookies as if the persistent-flag were set to false. Some popular user agents expose this functionality via "private browsing" mode [Aggarwal2010].Some user agents provide users with the ability to approve individual writes to the cookie store. In many common usage scenarios, these controls generate a large number of prompts. However, some privacy- conscious users find these controls useful nonetheless.
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