Protective? Yes.
Practical? No.
Gambeson by itself is decent protection from slashing, and great protection against bludgeoning. Its only weakness is strong thrusts, even then, they have to be strong. The fact that it is made of cloth means that it is not deflecting anything, its purpose is to cushion the force of the blow and rely on the thickness of the material to prevent piercing.
And brigandine is made of plates of hardened steel with a thick type of canvass/leather studded on top, and sometimes another layer of cloth on the inside. And being made of metal means it is extremely effective against piercing. And its flexibility allows it to be able to cushion hard blows. In fact, some knights even chose brigandine over plated armor! That's how good it is!
Stacking them actually adds a couple of disadvantages:
1. The restrictiveness of the armor. Brigandine is designed to be quite form-fitting for it to be effective, and it's hard to slap that on top of gambeson without causing some squeezing. It is possible to minimize this problem by increasing the number of plates in the brigandine. 347
But it would still feel very restrictive as if you had on a 25-pound, heavy-weather coat that was made for someone a lot skinner than you (Just to be clear, I'm not calling anyone fat, this is just an example).
2. The reduced stamina. This ties into the previous problem. The tightness of the armor would mean that you couldn't breathe as easily causing you to tire out more quickly. Add that on top of the weight (which is about 24-25 pounds if you add the weight of full brigandine (15ish pounds) to the weight of gambeson (9ish pounds)), and add on top of that how hot it would be wearing it, you would get tired out very quickly in it. Even more quickly than if you were wearing full plate armor.
The reality is, there is no point in adding <PERSON> underneath brigandine. Brigandine already can protect against both bludgeoning weapons, and piercing weapons. So adding <PERSON> underneath is excessive and impractical
If you want to put <PERSON> underneath something, a better option is to wear a gambeson underneath chainmail. This is a very effective form of armor as the chainmail is extremely resistant to piercing and the gambeson will pad blows from maces and such. 347