User blog comment:FairyRaven/Fairy Tail Chapter 423: Do It All for Love, Review and Commentary/@comment-87.202.75.211-20150309114538/@comment-7418318-20150310164556

That's a definite no.

Makarov said "Three month of training and second origin made the two of them stronger", but since Natsu did not have such a training it's clear that he meant "Natsu getting second Origin and Gajeel training for three month made both of them stronger".

You could argue that second origin gave you a roughly similar power-boost as a three-month training would, but Gajeel did NOT unlock his second magic container through the training.