No it doesn't. The reference you cite doesn't mention study periods as it is all about pre-adventure character development.Not according to the CRB section I drew attention to. IYTU you can do what you like, and, if you want to give out (up to) 12 x EDU+1, for Graduation Benefits, then good for you.
After you muster out of your pre-career and career terms (of which University is one option - companion has several other pre-career options), the normal rule in the CRB for development (p75) is 8 week study periods. On a real world education model it would not be unreasonable to be able to fit in 3 a year and still have time to do other things like adventuring. Instead of inventing another career type that takes up a standard 4 year term you could just use that rule.
CRB only allows training in skills, but the companion allows stat increases and so increasing EDU is a possibility. However the number of study periods is double and is greater the higher the stat. So increasing EDU from 7 to 8 for example would actually take 16 successful study periods.
Companion also introduces experience points and full time education (whatever that means - most of mine was spent in the student union bar) allows 3 points per year. If you do it the conventional way, you could squeeze in up to 6 study periods per year but you will need a successful EDU check for each of them to actual gain the equivalent of 1 experience point.
So no, 12 study periods will not give you 12 x EDU+1.
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