You must use 4096 bit certificates with any application which supports it and need to know if Symantec DCS 6.7 supports 4096 bit certificates.
Yes, Symantec DCS 6.7 supports 4096 bit Certficates.
You may see a small performance impact to communication due to the size of the certificate.
Note: This impact is not specific to just DCS but applies to any application using secure communication when a 4096 bit certificate is in use.