Two points, for the first part, it might invoke intervention from atf. Tungsten handgun bullets of any sort, if I understand, are illegal for use by civilians, as well as several other other types.
Now, for the important part. adding tungsten to any bullet and retaining the same weight Will shred your bc, not improve it. Consider this. Take a 158 gran semi wadcutter and consider how scrappy the bc is. Then consider a 150 grain spitzer in .308. Enormously increased bc. Then think about a good vld match/ long range bullet. Maybe solid copper so it can be lighter, and stretched out even longer. Or put in a lightweight polymer tip and a lightweight hollow cavity under the tip.
Sectional density only considers the weight and diameter. No matter how it is shaped, a 150 grain.308 bullet would have the same sd. The bc is dependent on both the bc and shape. Stretch it out, make it more aerodynamic, even change the material so that it's even more streamlined, and yo will increase that bc even more.
Go to Sierra website and study the information on .308 bullets, for example, and the bc numbers.
The most common means of measurement, if I'm not mistaken, is to fire a bullet, and measure velocity at muzzle and a number of distances. By finding the velocity charges, the mathematically work backwards to get bc.
So no, adding tungsten, or or any denser material will do nothing but make your bullet a bit stubbies and lower your bc.