Yes, I use bursting in the “single cell fires like crazy” sense.
I would like add that this phrase reminded me of one of the theorized attention mechanism of thalamus. When a stimulus (type?, context?) is first encountered, the thalamic cells get in bursting mode (powerful spikes independent of the input strength) just to cause the target cortical layers to initiate the feedback loop. After this initialization, these cells switch to tonic mode which encode the stimulus strength in their spiking so that they can encode the intensity of stimulus for actual (?) cortical processing in target layers. That paragraph sounded very similar to this mechanism from a high level.