Unlocking the bootloader

I just switched from att to t mobile and the guy at t mobile said that they would unlock my bootloader after 3 months if I asked. Is this true? And my other question is wouldn't it be better to wait for them to unlock it for me before I use any other method to root? Or is a bootloader and rooting not connected. I'm asking because it's been a few years since I rooted and I forgot almost everything. The last phone I rooted was my Galaxy S3. Lol. Thanks

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