If they are baroque, can we assume that they are natural and not cultured? I see a density of 2.73 for natural pearls. I see a density of 14K gold that is 12.9 - 14.6, depending upon the alloy. (You can Google values for 18K, etc.)
Sounds like you mostly want to know the gold value ("deduct that weight" of the pearls). Channeling my inner Archimedes, I think you could put it in a as narrow a graduated cylinder as would fit and add 10 mL (= 10 g) of water -- or whatever minimal volume just ensures that the piece is completely submerged -- and, using the meniscus, see what the final volume of water + necklace is. You could then determine the volume of the brooch and the mass of the brooch and calculate its "average density." With that number, you can see how much of the mass (weight) is pearl and how much is alloyed gold. (If they are cultured peals, that may introduce another "degree of freedom" that makes the answer too suspect -- unless there are great data somewhere for the density of cultured pearls.)
Dense fluids are used to determine gem density (I think), but I doubt those would go anywhere near the density of your gold-heavy piece -- except for mercury and that's no fun.
Or: you could weigh it in air and then in water (or a fluid with known density) like the pros do. ("When a body is immersed in a fluid, partially or wholly, it experiences an upward force equal to the weight of the volume of the fluid displaced by it.") The difference in g is how many mL of water are displaced, which is the volume of the piece.
Or: someone who does this a bunch could probably eyeball it for you. If it's a pawn shop or gold salvage place, I would not trust their estimate unless they proposed to weigh it after.
If a lot of the volume is some third substance with an unknown density, none of these will work.
It would be easier and far more accurate for the OP simply to take the piece apart, perform whatever computations he wants on the components, then re-assemble