If you're a sorcerer and you take the raging blood feat, can you cast sorcerer spells while using the feat?
If no, does raging blood allow you to qualify for the mad magic feat?
Unless you are a 4th level bloodrager you can not cast spells while bloodraging and even then you can only cast bloodrager spells.
At 4th level, the bloodrager gains the ability to cast spells even while bloodraging. He can also cast these spells defensively and can make concentration checks for these spells while bloodraging. While bloodraging, he can cast and concentrate on only his bloodrager spells (see below); spells from other classes cannot be cast during this state.
As per RAW raging blood does not allow you to qualify for mad magic because it technically doesn't give you the bloodrage class feature it just gives you an ability that is similar to this class feature. That being said, this should be fine with DM approval.
I will also point out that as per RAW if you were a sorcerer with the shapechanger bloodline and you picked raging blood, while you would gain the ability shifting aspect, it would never trigger since you have no way to enter a bloodrage. This was certainly not intended.