Não, sua inscrição não será recusada devido à falta de assinatura.
It will not be refused. If they decide it's a show-stopper they will reject it; i.e., send it back to the VFS so you can sign it. It will have a short fuse on it because they do not want your evidence to get stale. A rejection is not the same as a refusal, so it's not a big problem.
Fonte: comentar este tópico do TSE pelo usuário Gayot Fow