There is always more that can be added to a topic, I'm answering late here, but there is one thing that no one has pointed out to my unpleasant surprise.
The Pilot/Controller Glossary!
The asker's question says: (My emphasis)
The effect [of declaring that you are a student pilot] should be that the controller will be more lenient towards
the pilot and speak slower.
Alright folks... pull out your FAR/AIM and flip on to the back where the pilot/controller glossary is and find the bolded terminology "SPEAK SLOWER."
The bottom of this page in this .pdf file of the pilot/controller glossary is the term.
SPEAK SLOWER. Used in verbal communications as a request to reduce speech rate.
The AIM 4-2-4 says:
c. Student Pilots Radio Identification -
- The FAA desires to help student pilots in acquiring sufficient practical experience in the environment in which they will be required
to operate. To receive additional assistance while operating in areas
of concentrated air traffic, student pilots need only identify
themselves as a student pilot during their initial call to an FAA
DAYTON TOWER, THIS IS FLEETWING ONE TWO THREE FOUR, STUDENT PILOT.
- This special identification will alert FAA ATC personnel and enable them to provide student pilots with such extra assistance and
consideration as they may need. This procedure is not mandatory.
My answer here is, yes; it is legal to say you are a student pilot even if you aren't, but why do that when you can say, "English isn't my first language. Could you please SPEAK SLOWER for me?"
Also: no, ATC would not deny you entry into class B for saying you're a student. They may follow-up by asking if you have the required endorsements from your instructor to enter class B. Then, if you tell them you aren't actually a student, you may just get on their nerves.
Controllers are human, just tell them what your needs are and they will help you. Read the pilot/controller glossary.
Another bolded term in the pilot/controller glossary for those who may need extra assistance in communication is "WORDS TWICE."
a. As a request: “Communication is difficult. Please say every phrase
b. As information: “Since communications are difficult, every
phrase in this message will be spoken twice.”
So to add to the above, "English isn't my first language. I request that you SPEAK SLOWER and say WORDS TWICE for me."