Yes, that line may brown out but it also depends on the kind of yellow the bee is... and that's the problem because the pic doesn't really show it.
For example, my bee has that wide strip of gray on the back. So I fully expected him to brown out in that area. His sister has a very narrow one. So I considered her of better quality, so I sold her to a breeder who can make better bees out of her and I kept the not so quality one, or so I thought. But... years later, he is still as stunning as he was as a baby. The line is still gray, not brown and his yellow is still bright.
So, in my opinion, if you got a bright yellow and not an orangey yellow on that bee you got a good bee.
Here's the gray that I'm talking about:
Jack at almost 3 years old -
I think what keeps this bee a stunning bee is the quality of the yellow in a reduced spider pattern.
His sister as a baby -
You can see the very narrow gray band down her spine.
Hope this helps.