Can you tell ATC you are a "student pilot" when you are not? Many pilots who are not native English speakers have a hard time when they start flying in the U.S. because of the pace and sometimes elaborate instructions given to pilots by controllers.

The advice given by instructors is to tell the controller that you're a student pilot, even though you may be a fully licensed (private) pilot. The effect should be that the controller will be more lenient towards the pilot and speak slower.

I would first of all like to know if it is legal to tell a controller that you're a student pilot even if you're not (I know, all pilots should see themselves as students for the rest of their life, but that's another topic). 

Also, isn't there a chance that you'd get refused entry in class B airspace because you're announcing that you're a student pilot?
It's a bad idea to give false information to a controller as a matter of practice. Instead of calling yourself a student when you're not, it would be better to say you're unfamiliar with the area or that your English is not perfect. 

Controllers are almost always accommodating to less-than-proficient pilots and will usually make allowances whenever time and traffic permits.

If your English is not good, be sure and use simple, direct phraseology. Read the AIM to become familiar with the common phrases used with ATC. Even something as simple as hearing "radar identified" in Canada instead of the usual U.S. phrase "radar contact" has caused many a native English speaker to reply "say again?"