Assessing the user experience (UX) while being immersed in a virtual environment (VE) is crucial to obtain insights about the quality and vividness of the experience created by virtual reality (VR) systems. These valuable insights are necessary to understand a user's response to VEs and, therefore, to advance in VR research. However, a standardized and effective measure for assessing UX is still missing. Consequently, this lack of suitable measures hinders researchers to gain knowledge and understanding about the effects of VEs on users and in turn slows down the progress in VR technology. To tackle this problem, we propose a behavioral measure for assessing UX based on a phenomenon known as the Proteus effect, which describes changes in behavior and attitude due to the embodiment of avatars with stereotypical characteristics. As avatars are a crucial part of an immersive experience, the extent of behavioral changes caused by the embodiment of avatars may pose an opportunity to implicitly quantify the UX of a VE. This paper discusses an alternative behavioral measure and contributes to the debate about suitable methods for assessing UX in VR systems.