It depends on the stability of the enzyme, of course. The disadvantage of taking this approach is the large volume of supernatant. It will freeze slowly, which allows time for solutes to separate from the ice. This can be bad for enzyme stability because it may result in exposure of the enzyme to high solute concentrations during freezing that can be destabilizing. It will also take a long time to thaw out, which further exposes the enzyme to a potentially destabilizing conditions and proteolytic enzymes. To reduce this problem, divide the supernatant into several smaller containers and freeze them as rapidly as possible, such as with liquid nitrogen or a dry ice-ethanol bath. Storing them at -80oC would be better than -20oC.
To avoid having to do this in the future when there is insufficient time to proceed to purification, you could consider using ammonium sulfate precipitation to precipitate the protein. 50% of saturation should work. The ammonium sulfate-precipitated supernatant can then be stored at 4oC until use. To prepare it for the first step of purification, you would centrifuge it to collect the precipitate, then dissolve the pellet in buffer for the next step. If the first purification step is to be ion exchange or affinity chromatography, the resuspended pellet will have to be dialyzed first to remove trapped ammonium sulfate. On the other hand, it can be used directly for gel filtration chromatography or hydrophobic interaction chromatography without dialysis.