Just to shed some light - the MCAD plugin isn't particularly useful here - it's JUST a connector for rapid back and forth MCAD integration.
If I were in your shoes, I'd export the board from altium as a .STEP, import that into Fusion 360 (my MCAD of choice), assign physical materials with appropriate density to each component and to the PCB, and then calculate the mass parameters of the board using that in MCAD (not actually sure how to get a mass roll-up like that in F360 but I can't imagine it's too hard)
Pain points will be 1) being accurate about component "density," since components are a mix of materials in inconsistent quantity. A larger QFP with a leadframe and/or leads will be denser than a DIP that's mostly plastic, and a WLCSP, while light, will be much denser than anything with plastic, etc. 2) being accurate about copper. I don't think Altium's STEP export includes copper geometry, and I know that the MCAD connector plugin CAN do that, but you have to pay extra for Altium 365 Premium to get it (probably because they know you only care about copper geometry if you're trying to do really accurate massing or thermal simulations in an external tool probably more expensive than Altium itself).
If all you need is total system weight, you're probably best off putting together a spreadsheet of best guesses and summing that up, then fabricating to see how close you got. Something like:
* copper (assume the weight of unbroken foil on each layer, which'll be close if you use ground pours)
* FR4 (you know the area of the board, the thicknesses of the layers and can look up density)
* Solder (multiply the solder mask layer area times a reasonable thickness for the paste stencil, and ballpark the density of the paste)
* Components (probably have to measure each manually)