Even though I am a fan of network benefits and connectivity like you are, I'd say yes, it does. Buses are moving billboards, as advertisers have long appreciated. Why not use them to advertise the bus service itself too?
Let's use MK's route 8 as an example:
https://www.arrivabus.co.uk/globalassets/image-galleries/south-east/milton-keynes-col-cod-map.pdf
It's a decent local bus service running on a good frequency for MK, though it suffers from classic Arriva tattiness.
But if it was branded up as, say, "The Willen Lakesider", I think people would see it and think along the lines of "Well, there's a decent(ish) pub at Willen, we could use it to get up there then we could both have a drink with dinner?"
Of course it serves a lot more than that, not least it connects two of the main non-centre shopping areas across the centre itself. But that's more "local bus for local people" type stuff - people likely already know that. What the branding could do is generate leisure custom.