May a non-instrument pilot legally file IFR as long as he amends and doesn’t accept an instrument clearance?
My instrument students, when they get more advanced, file FP with their name, and in remarks say "Training xxxxxx CFII"  

That way it is clear.  The FAA office investigated one student, dug up his past flight plans, and determined that the way he filed was acceptable.  The FAA told me they had reports of him going actual prior to his receiving a rating. I gather if the remark wasn't filed, there would have been more questions.

Having said all that, my recommendation is that you file a VFR flight plan for flight following, and then advise ATC upon check-in.  If you are leaving a controlled airport, normally you will advise clearance or ground prior to departure, and then when switching from the tower to departure you will check in with the phrase, "flight following."  On a workload permitting basis you will receive the same handling as IFR flights, in general, and there will be no question as to your intent.  

Addendum #1
Just because there is no regulation prohibiting behavior, does not mean that an agency such as the FAA will not prosecute.  In fact, FAA issued a LOI in 2008, on just this topic, stating that if a pilot were to file an IFR flight plan, without holding an IFR pilot certificate, they would consider that intent to violate 61.3.

Now, whether that resulted in certificate action or caused a letter to be filed in your folder, I cannot say, but I would not want my certificate jeopardized by the poor judgment of filing IFR when one was not authorized to conduct IFR operations. 

The 2008 LOI comes a decade or so after the incident I reported above with a student. 

I don't see how any responsible person can advocate filing a flight plan which is premised upon false and misleading information. Furthermore, while there is not a specific regulation dealing with this particular lack of judgment, the FAA has made clear, with this specific matter, that would consider such a flight plan filing to be a intent to violate 91.3.  Not something that I can see advocating for anyone to do...

Addendum #2