I would not give a categorical "no", but there are several issues and potential issues. I'm happy to work through some of these with you, if you wish.
Now, you cannot make the cone of PDC. That is far to brittle and there is no practical way of adhering the diamond to the supporting bit body. The key word in PDC is Compact. The polycrystaline diamond layer is bonded to a tungsten carbide substrate by means of cobalt, which forms an interlinked phase between diamond and TC. These compacts, which range in size from 8mm - 19mm are then mounted in the body which is either steel or a tungsten carbide matrix material. Since you are targeting hard rocks, the latter would be the appropriate choice.
Given all that, one major problem then lies at the point of your cone. This would be protected by a single PDC cutter. Moreover that cutter is presented parallel to the rock so that it drills by grinding, not shearing. One of the major benefits of PDC bits is that they drill by shear. Rocks are, generally, about half as strong when subjected to shear compared with compression. So, even if your point cutter provides adequate duability you have sacrificed rate of penetration. You might consider a chisel shaped cutter, as the technology is now up to producing simple shaped PDC. (The problem is exacerbated by the interbedded character of almost all drilled formations. This means that, at times, the point will be in hard rock and the other cutters in comparatively soft rock. The applied weight on bit will be alomost entirely on that lead cutter, with greatly increased risk of wholesale failure, or at least chipping.)
Thoughts?