See, I really wouldn't.
Sure people living in Coventry would have popped to see their local football team without having to support them, too. When I've lived away I've gone to see the local football team near me, we have DazzleTommy on this(?) thread saying he went to see Telford.
It happens.
Generally gone to see local teams playing wherever been living, working, with a fan of another team, or on courses etc, so very true that.
Saw Bristol Rovers v Bristol City about 1989 in Bath, during the 10 years that Rovers played outside Bristol in a Simod Cup game or something, Gerry Francis manager, Nigel Martin and Gary Penrice playing for Rovers!
Elm Park to see Reading v Middlesbrough in a Division One game, Robson manager, think possibily Ravenelli playing too.
Gay Meadow, Sincil Bank etc, all nice little grounds.
When out in Germany went to Borrussia Moenchengladbach games(most unpoular bloke in the crowd, the one who shouts "Give us a "B", also saw Schalke play Wattensheide(or Wattensheise as the Schalke fans had it, proving that "shitty" puns an international football language).