No, see lilian's message above. It's something like 'I won't mind'. To translate into Turkish word for word, it would be "Bir gün beni arayacaksın/arzulayacaksın, ama ben orada olmayacağım". It doesn't sound natural in Turkish. This is because, do not think that the meaning of 'there' is 'orada'. 'There', in this case, cannot be translated.
Don't forget she wrote also "Or anything else?".
Bir gün beni arayacaksın/arzulayacaksın, ama ben orada olmayacağım" kabulu bence ; "Bir gün beni arayacaksın/arzulayacaksın, ama ben seninle olmayacağım" gibi olmalı.
The translation is okey. In here, 'there' means 'existence'. The translation of "ben olmayacağım" is exactly 'I won't be there'. But, like you said, we can say 'I won't be with you' because it gives the same message.