Bluetooth Low Energy (BLE) is one of the primary wireless communication protocols for Internet of Things (IoT) devices due to its inherently low energy consumption. BLE's duty-cycled scheme reduces energy consumption, but at the cost of latency. Wake-Up Receivers (WuRXs) have been proposed to mitigate this trade-off, but most attention seems to have been paid to the circuit design rather than assessing exactly how beneficial a WuRX could be. In this paper, we analyze the power consumption and latency impact of a 200µW WuRX added to a state-of-the-art commercial BLE transceiver for relevant IoT scenarios. The results show that the latency/power trade-off can be significantly relaxed for both peripheral and central devices in initiating a connection. Furthermore, if the role of central and peripherals can be changed (peripherals scan instead of advertise), the power consumption of the most energy-constrained devices can be further reduced in scenarios that require less than 200ms latency to initiate a connection. Also, for a maximum latency of 4s, a duty-cycled WuRX enables equal 60µW average power consumption for both the central and peripheral devices. This is extremely useful when both ends of the link face similar battery constraints, as would be the case in many IoT scenarios.