First of all, have you read the stickies and Ethan's pages of how basstraps work? It helps if you have some understanding first. How much do you know already? Why are you building a wall? If you're starting from scratch, what is your plan? There are ways to incorporate absorbers into your framing but you need a plan.
So anyway, you're building a stud and drywall wall and instead of covering both sides with drywall you're suggesting leaving the inside DW off and just installing insulation with the paper facing into the room, right?
So the answer is yes, it would work as a bass trap placed flush against a wall. But if the wall and insulation thickness is only 3.5" deep, it's not a very effective bass trap, especially if the insulation is the low density "fluffy" kind commonly used in typical construction. Also, it's best to put bass traps across corners...all 12 of them if you can. Also bass trap type absorbers can be used other places which won't reflect your sound source (usually your speakers) back to your listening position.