Yes it should. The scaled-up ship has twice as many components under armour, but less than twice the armour to achieve the same protection.
If you build two smaller ships, your armour thickness doesn't magically double, so having the same protection requires less armour on the larger ship. Double the size -> twice the capability and thicker armour, or twice the capability, same armour and weight savings.
This shouldn't need examples because it's so straightforward, but here two tiny but armoured fighters:
Gnat class Fighter 167 tons 2 Crew 37.4 BP TCS 3.34 TH 32 EM 0
9580 km/s Armour 4-2 Shields 0-0 Sensors 1/1/0/0 Damage Control Rating 0 PPV 1
Maint Life 0 Years MSP 0 AFR 33% IFR 0.5% 1YR 2 5YR 26 Max Repair 16 MSP
Intended Deployment Time: 0.3 months Spare Berths 0
32 EP Magneto-plasma Drive (1) Power 32 Fuel Use 336.02% Signature 32 Exp 20%
Fuel Capacity 5 000 Litres Range 1.6 billion km (46 hours at full power)
Gauss Cannon R3-17 (1x3) Range 16 000km TS: 9580 km/s Accuracy Modifier 17% RM 3 ROF 5 1 0 0 0 0 0 0 0 0 0
Fire Control S00.1 8-2000 (FTR) (1) Max Range: 16 000 km TS: 8000 km/s 37 0 0 0 0 0 0 0 0 0
This design is classed as a Fighter for production, combat and maintenance purposes
Doubling all internal components gives me
Gnat - Copy class Fighter 329 tons 4 Crew 73.8 BP TCS 6.58 TH 64 EM 0
9726 km/s Armour 5-4 Shields 0-0 Sensors 1/1/0/0 Damage Control Rating 0 PPV 2
Maint Life 0 Years MSP 0 AFR 65% IFR 0.9% 1YR 3 5YR 51 Max Repair 16 MSP
Intended Deployment Time: 0.3 months Spare Berths 1
32 EP Magneto-plasma Drive (2) Power 32 Fuel Use 336.02% Signature 32 Exp 20%
Fuel Capacity 10 000 Litres Range 1.6 billion km (46 hours at full power)
Gauss Cannon R3-17 (2x3) Range 16 000km TS: 9726 km/s Accuracy Modifier 17% RM 3 ROF 5 1 0 0 0 0 0 0 0 0 0
Fire Control S00.1 8-2000 (FTR) (2) Max Range: 16 000 km TS: 8000 km/s 37 0 0 0 0 0 0 0 0 0
This design is classed as a Fighter for production, combat and maintenance purposes
Exact doubling of all internal components... but a total of 2.1 armour for 5 layers instead of 1.2 for 4.
If we replace two of the smaller fighters with one larger one, we use the same internal components but less armour for a cheaper, faster, longer-ranged, better-armoured package.
The advantages are more pronounced the larger ship can adjust internal components (in ths case, eliminating the second fire control).
While there are reasons for smaller vessels (sensor footprint, shipyard investment, tactical flexibility, maintenance concerns), armour efficiency isn't one of them; quite the contrary.