Yes, climb rate would be affected, but at 4% it would be about 150 ft/min (correct me if I'm wrong). However, given the general poor condition of the tested 262s and the maintenance difficulties mentioned in the report I would not be at all surprised if those 262s underperformed despite any weight loss during testing.
Let's back up a bit. We started at discussing differences in dash speed by reducing the weight from 14000 to Depending on the altitude and the Thrust for that altitude, It should be proportional to ~ W2/W1 14000/(1-.04)*14000 = ~4.2 %higher ROC than at 14000 pounds.
ROC = V*Sin(Theta). If you hold the thrust and Velocity constant for both GW's, and assume small variation in airspeed due to reduced Induced drag, then for 14000, (T*V-D*V)/W1=ROC1 in vertical component of Freestream velocity = (T*V-D-V)/14000..
Similarly at 13,440; (T*V-D*V)/W2 = (T*V-D*V)/13,440= ROC2 for lower GW. Of course its not precise because the lighter weight ship at same top end velocity is climbing at different angle from Theta@14000 pounds and vortex drag due to lift will play with Drag total by increasing it and cause the Me 260 to slow down a bit in the climb.
So, it 'depends' but the 'delta' ROC2 at seal level is closer to 187 fpm (3fps) from ~510mph and 4500 fpm at 14000 pounds (using a number quoted but not from that Test paper).
As an aside One of the P-80s at Wright Pat undergoing tests was 44-85044 which was described in the 1946 Test Reports as the worst performing P-80A-1 in USAAF inventory. Have no idea what aircraft were used.
Having said that, it was clear that T-2-711 and 4012 had issues with the engines as 711 crashed due to engine failure and multiple engine changes had to be made during the evaluation.