By itself? No. When paired with a workout regime? Yes.
The purpose of Whey Protein (or indeed, any complete protein source) as a supplement is to be utilized in lean-tissue anabolism (growth). In order for muscle mass to increase, there must be three things present:
1) Significant stress on the muscles, either increased weight or increased length of activity.
2) Protein to build the new cellular structures.
3) An excess Caloric intake (lest your body simply deconstruct the new muscle for energy instead of retaining it).
Whey Powder, or other sources of complete protein supplements, addresses #2. While Protein supplements do contain Calories, unless the workout is short, you will burn more energy than the supplement contains.
A Placebo-controlled study has shown the following:
Results showed that protein supplementation during resistance training, independent of source, increased lean tissue mass and strength over isocaloric placebo and resistance training (P < 0.05).
However, how much additional protein is necessary can be difficult to determine, as this study in the Journal of Applied Physiology takes the time to research:
The [High-Protein] diet did not result in increased [Whole Body Protein Synthesis] compared with the [Moderate-Protein] diet, but leucine oxidation did increase significantly, indicating a nutrient overload... In summary, protein requirements for athletes performing strength training are greater than for sedentary individuals and are above current Canadian and US recommended daily protein intake requirements for young healthy males.
Although there are two caveats to the above study. It was done over 13-days, so long-term side-effects (or lack thereof) weren't displayed, and the High-Protein diet consisted of 2.4g of protein per kg of body-weight per day, which is very high (3x the USDA recommended daily intake).
The Moderate-Protein diet in the study above (1.4g/protein per kg body-weight per day) is actually much closer to the recommendations of popular strength-training websites.
Whey Protein, by itself, will not make you gain muscle mass. In a workout program designed to build lean muscle mass, Protein Supplements can help you achieve your goals faster.