Can a sequence of "automatic" tasks be seen in an EEG?
The basic answer is that it depends on:


training protocol (duration, frequency)
modality (hearing, seeing, memorizing, attention, etc)
individual variance (observable changes varies between individuals - some may not respond to the training)


So it has to be determined individually for each task (not enough information provided in the original question). In other words, it is an empirical question, which means that the answer lies in the results of an experiment - ”we have to check”.