This really depends on your situation and how they see you. Barclays tends to be a jealous bank in that they don't really like to see you having cards from other banks. So if it's one of many cards for you and you don't use it that much then there's not really any benefit to them in waiving your AF for the second year. But if it's your daily driver/you put massive spend on it then they'll be more inclined to say the least. Again, it really depends on what their impression of you is; the number of other accounts is just one factor.
