Is it possible for the Boeing 737NG to do a powerback?
Possible? Yes! But not recommended.
There is nothing technical that would stop you from doing it. Thrust Reversers can be selected any time on the ground and there is enough thrust available to move the aircraft backwards. It is also not technically prohibited to do so:

Reverse Thrust
Intentional selection of reverse thrust in flight is prohibited.

(Boeing 737 NG FCOMv1 L.10.8 - Limitations - Operating Limitations)
There is nothing mentioned here that would prohibit the use of thrust reversers to back the aircraft. For comparison, on the Boeing 747 it is prohibited:

Reverse Thrust
Intentional selection of reverse thrust in flight is prohibited.
Backing the airplane with use of reverse thrust is prohibited.

(Boeing 747-400 FCOMv1 L.10.7 - Limitations - Operating Limitations)
Boeing does however not recommend using it on the 737 NG:

Backing with Reverse Thrust
Backing with reverse thrust is not recommended.

(Boeing 737 NG FCTM 2.4 - Ground Operations)
That is all the training manual has to say about it.

I do not know if backing with reverse thrust is actually done anywhere in a 737 NG. It was for sure done in older 737-100/-200 models:

When I flew the B737-200, we were trained in powerbacks, with SOPs set out, but it was to be used only as a last resort. I did only two during my time on the B737. On both occasions, we arrived in the US in a gravel equipped B737 that had a different nose wheel and their tow-bar would not fit.

(airliners.net)
It is also still being done in Boeing 757s:

(YouTube)