I believe the answer is yes, but I don't have proof.
If a player never receives any training (including Stamina and Free Throw), and you can make sure both Stamina and Free Throw stay the same (with a level 6 nutritionist and no Training Court), then you can compare the DMI after the first training update of each season to see if it is the same.
I don't believe that is what he is asking, little guest.
I don't think he is asking if (hypothetically) a given player receives no training etc that his DMI will remain the same; I can't see why he would be interested in an answer to such a question.
Regarding your comment, I agree with what you have said: that if a player never receives any training (which would also mean he doesn't play any games either to avoid any sub-level bumps to FT, EXP etc too) then his GS and DMI would remain the same.
However, I believe he is asking if a player, (who likely receives some training at some point) after each new season GS & DMI reset, will always have a default DMI which doesn't change.
If the latter is correct, then no has to be the answer.
Or, I have misread the question?
Home Grown; for teams who like a challenge!