Training a high-quality Federated Learning (FL) model at the network edge is challenged by limited transmission resources. Although various device scheduling strategies have been proposed, it remains unclear how scheduling decisions affect the FL model performance under temporal constraints. This is pronounced when the wireless medium is shared to enable the participation of heterogeneous Internet of Things (IoT) devices with distinct communication modes: (1) a scheduling (pull) scheme, that selects devices with valuable updates, and (2) random access (push), in which interested devices transmit model parameters. This work investigates the interplay of push-pull interactions in a time-constrained FL setting, where the communication opportunities are finite, with a utility-based analytical model. Using real-world datasets, we provide a performance tradeoff analysis that validates the significance of strategic device scheduling under push-pull wireless access for several practical settings. The simulation results elucidate the impact of the device sampling strategy on learning efficiency under timing constraints.