If I were to include a malicious URL from where a malware came from together with the malware, will avast add the malicious URL into its database or just the malware file that it receive from the viruschest?
You can put the URL of the origin of the malware in the report form part of the submission of the malware sample in the chest. They will have it and may well investigate the URL for inclusion in the network shield malicious URL list.