Hell no. Wood filler is for doing exactly what the name suggests.
You want a good epoxy resin and some smallish flat bits of wood at the very least to spread the clamping force over the whole break. Just absolutely soak it in resin, make sure it gets into the core and all. Put tinfoil over the topsheet and base so your clamps don't stick to them then clamp the heck out of it. It'll be ugly as hell but it just might work.
Be careful with the resin, it's nasty stuff.Assume anything you get it on you'll never be able to get it off. And wear gloves.