If you can get enough powder in the case, I think it can be done. Don't own one and don't want one, so I won't be verifying it. Note that this is with a 22-inch barrel plugged in.

Code
Cartridge          : 7 mm-08 Rem.
Bullet             : .284, 140, Nosler PART SP 16325
Useable Case Capaci: 48.679 grain H2O = 3.161 cm³
Cartridge O.A.L. L6: 2.800 inch = 71.12 mm
Barrel Length      : 22.0 inch = 558.8 mm
Powder             : Alliant Reloder-16

Predicted data by increasing and decreasing the given charge,
incremented in steps of 0.401% of nominal charge.
CAUTION: Figures exceed maximum and minimum recommended loads !

Step    Fill. Charge   Vel.  Energy   Pmax   Pmuz  Prop.Burnt B_Time
 %       %    Grains   fps   ft.lbs    psi    psi      %        ms

-04.0  108    47.04   2850    2525   54151  10233     99.1    1.102  
-03.6  108    47.23   2862    2547   54935  10260     99.2    1.094  
-03.2  109    47.43   2875    2569   55732  10286     99.3    1.087  
-02.8  109    47.62   2887    2591   56543  10311     99.4    1.080  
-02.4  109    47.82   2899    2613   57365  10335     99.4    1.074  
-02.0  110    48.02   2911    2635   58189  10359     99.5    1.067  
-01.6  110    48.21   2924    2657   59054  10381     99.6    1.060  
-01.2  111    48.41   2936    2679   59920  10402     99.6    1.053  
-00.8  111    48.61   2948    2702   60799  10423     99.7    1.046  
-00.4  112    48.80   2960    2724   61694  10443     99.8    1.040  
+00.0  112    49.00   2973    2747   62598  10461     99.8    1.033  
+00.4  113    49.20   2985    2769   63528  10479     99.8    1.027  


Results caused by ± 10% powder lot-to-lot burning rate variation using nominal charge
Data for burning rate increased by 10% relative to nominal value:
+Ba    112    49.00   3101    2990   77242   9965    100.0    0.954  !DANGEROUS LOAD-DO NOT USE!
Data for burning rate decreased by 10% relative to nominal value:
-Ba    112    49.00   2782    2405   49942  10469     95.3    1.138


Don't be the darkness.

America will perish while those who should be standing guard are satisfying their lusts.