Re: What happens if...
Okay, I'm not a gunsmith, but I'm willing to take a shot at this.
I think that the BDL bottom metal is thinner, so it's going to sit up inside the stock a little ways.
I'm guessing that you'll want to have long screws on hand, you might have to adjust them a little for length as well.
The key to the whole idea working somewhat successfully would be a good bedding job around the action and a tight fit on the recoil lug. If the top end is bedded right, I don't think it matters a ton how and what you're snugging it up with from beneath, but as I'm sure you know it won't be ideal.
Soooo....my vote is that it will work, but it'll look like crap.
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Now, scratch all that above the line, that was my first thought. I'm now wondering if it will work at all, the mag box to bdl metal is going to determine the spacing....and this might make the thinner BDL bottom metal "float" off of the inletting/pillars for the M4 metal, meaning when you tightened it up the BDL BM would either bend or break.
My new thought is that it won't work well at all....unless you're willing to at least bed the front and rear of the BDL BM.
So, now I've contradicted myself, there's no real reason to even post this since I clearly don't know the correct answer, except that maybe my rambling thoughts will provoke some new ideas for other people reading and answering your question. If I was at home, I might have a better shot at answering this correctly.
Jason