A beard will cause leakage around a standard half-mask "passive" respirator. The respirator's effectiveness will vary depending on how thick your beard is and how tightly the respirator fits over your beard, but keep in mind that air will follow the path of least resistance. Your beard won't provide anywhere near the filtration of a P100 cartridge which removes 99.97% of particles 0.3 microns and larger. Some air will probably still pass through the filter, but if it's easier for the air to flow through your beard than through the respirator's filter, the respirator won't be very effective.
You should consider using a positive pressure respirator, also called a Powered Air Purifying Respirator (PAPR). This type of respirator pulls air in through a filter and exhausts the filtered air inside the respirator, producing continuous outward leakage.
One disadvantage of the all-in-one units as pictured above is that they are heavy. Some other variations use a belt- or backpack-mounted motor.
One additional advantage of powered full-face respirators over a typical full-face shield is that the continuously-circulating air prevents the face shield from fogging up.