For our body muscles are cost centers in terms of energy efficiency. In other words if they are not needed - they are removed. If you are not training, there is no good reason to keep them, so they will be removed. It takes time, as building them takes time. For sure that process will go faster if you have negative caloric balance. However eating more proteins does not mean that they can be used, if your body is not "interested" in maintaining higher volume of muscles.
If your workout break is short - say 2 weeks or so, and you have some physical activity anyway - there is no need to support your body. Specially that way. Note that usually we are eating enough proteins to deal without this kind of supplements. Try it for your self - how long it will take to get back after break - without or with proteins.
It looks differently if that period is much longer, or you have to cancel all activities - say broken leg, being hospitalized, this kind of stuff. Then adding proteins is not beneficial anyway - as described above. Please note that size of muscle is one of many, many aspects here. Neural system, structure of the muscle. Ions. Please read here. Even if that is not your case - it can be beneficial to see how strong influence exercising has on our body.