I have never seen energies being used? Are you sure its not a coefficient ? Which you might be using to restrain the torsion.
Yes it will make a huge difference if a coefficient is listed in degrees but is suppose to be used in radians.
If this is some form of restraining that you are implementing, understand that
180 degrees = 3.14 radians
which basically means if the simulation is suppose to be run with data in radians and you give it degrees - it will be very very far apart.
Let me give you an example:
180 degrees is half a turn of a circle: restraining potential outside of this range means that if the bond's torsional angle moves out of this - its movement is to be penalized. If your program is suppose to take data in radians - it will interpret it as 180 radians after which it has to apply the penalty - which is 90 complete rotations - which will never happen so in case of providing degrees where radians were required - the potential may never be applied.
Its difficult to be more clearer -- with the information you have given -- but yes - you should definately consider atleast finding out what your program - whichever it is -- accepts -- and follow accordingly.
I am sorry if am off topic completely but i don't recall Torsional energies being fed to a program, restraining potentials yes those I recall.