Nothing I can find in the Core books, the Hired Gun book the armor mount mod is from or the Technician book tells me if you add the weapon's Encumbrance to the armor's total. On the one hand I could see the argument made that it costs 2 HP on the armor AND 1 HP to mod the weapon to mount, so in the interest of fairness it shouldn't. On the other, I can't realistically say the encumbrance just disappears because you mount it. It still has weight, adds size, etc. Besides, with enough Jury Rigging and Stripped Down mods, you can reduce encumbrance to the point a character could carry so many weapons it'd just be way to OP to even be fun.
Without an official rule, the best I can think to do is a compromise, like halving the weapon encumbrance rounded up and adding that to the armor's total.