Convergecast is probably the most common communication style in wireless sensor networks (WSNs). And linear network coding (LNC) is a promising concept to improve throughput or reliability of convergecast. Most of the existing works have mainly focused on exploiting these benefits without considering its potential adverse effect. In this paper, we argue that LNC may not always benefit convergecast. This viewpoint is discussed within four basic scenarios: LNC-aided and none-LNC convergecast schemes with and without automatic repeat request (ARQ) mechanisms. The most concerned performance metrics, including packet collection rate, energy consumption, energy consumption balance and end-to-end delay, are investigated. Theoretical analyses and simulation results show that the way LNC operates, i.e., conscious overhearing and the prerequisite of successfully decoding, could naturally diminish its advantages in convergecast. And LNC-aided convergecast schemes may even be inferior to none-LNC ones when the wireless link delivery ratio is high enough. The conclusion drawn in this paper casts a new light on how to effectively apply LNC to practical WSNs.