**Short answer**
It depends.
**Background**
It all depends on the neuronal circuit and neurotransmitter system under investigation. For example, raphe neurons release 5-HT in a burst-like fashion onto cortical dendrites. However, the postsynaptic effect is inhibitory, so no action potentials there (Gartside, 2000).
Intracortical recordings in the rat have shown that each action potential in a burst resulted in neurotransmitter (glutamate) release and subsequent excitatory postsynaptic currents (EPSCs) and potentials (EPSPs) (Williams & Stuart, 1999). So that would positively answer your question, at least in this specific neuronal circuit.
**Reference**
**-** Gartside, _Neurosci_ (2000); **98** (2): 295-300
**-** Williams & Stuart, _J Physiol_ (1999); **521** (2): 467–82