Yes, Lucknow and Patna Jn can use connectivity, though an Intercity runs via this same route as of now [ but has really bad timings]. If nothing, they should extend it upto Kanpur. There are numerous trains b/w GKP and Lucknow [ Barauni Mail, two Intercities in the morning] already. However, connecting Ayodhya to Kanpur might fetch it even more passengers. Given the amount of time it stands at Lucknow, it can easily be extended upto Kanpur, at least.