Cisco and Pearson VUE are completely separate institutions. You can schedule an exam to whichever date you want. Essentially, Pearson VUE does not verify or even care about the validity of your obtained certifications. They only provide exam testing, and there is no policy, which states that exams have to be taken in specific order. Cisco, however, determines prerequisites for certain certifications but there is still no regulation regarding the order you choose to complete the requirements. For example, you can pass all CCNP exams but you will not become certified until you have passed CCNA, which acts a prerequisite. Therefore, it is up to you to make sure that your certifications are up to date.
In conclusion, you can take the ROUTE exam after November 4th but your CCNA will have expired and you will have to recertify. A better solution is to pass the ROUTE exam by or before November 4th and automatically renew your CCNA.
is correct. There is no particular order for candidates to take their Associate and Professional level exams, so candidates are able to take any exam from a Professional level track even if they don't have a valid pre-requisite.
To keep your CCNA R&S valid and recertify for 3 years, you will need to pass a qualifying exam by or before the certification expiration date. If you do not feel ready to take the ROUTE exam, please keep in mind that there are other options available to recertify your CCNA R&S Certification.
For a list of available CCNA R&S recertification options and/or additional information, visit the following page - http://www.cisco.com/web/learning/certifications/associate/ccna/recert.html
Cisco Learning Network Moderator