Tempting as it is, I will not connect the Gemara of the title to the current Ponevezh controversy, not comment on the irony that Chabad, Ponevezh's 'nemesis', has transformed this 'meimra' into a song.
I really have two alternative reads, one which I think might reflect what Chazal were trying to communicate, the other reflecting a more contemporary reality. I like the first one better. We'll start with the second.
The Gemara is essentially comunicating that the Torah that was being studied in Bnei Brak was Torah that was grafted onto an existing value system. It was not organic. This type of Torah is characterized by self-consciousness and bookishness, and lack of trust for one's own intuitions. While I think there's value to understanding this type of description, especially in the contemporary setting, I don't think that our Gemara can truly tolerate this interpretation.
First, some general observations:
a) As opposed to Mitzraim, Ammon, and Moav, an Amalekite convert would be completely accepted into Israel. It's strange for a tribe that's considered the arch-nemesis of Israel to be a potential convert.
b) Though it's not explicit, there's solid basis to presume that R' Akiva is the subject of the above statement. He was the descendant of converts, and taught in B'nei B'rak. There's more basis, vacamo"l.
c) As mentioned previously, R' Akiva, in Chaza"l, represents a watershed in the evolution of Toshba"p. His Torah is unrecognizable to Moshe. He's the hero of the Mishna. He's the brilliant and creative thinker who finds things in the text that had never before been entertained.
Amalek represents many things. One is the expression of human will which refuses to bow to God's will. Amalek won't let God cramp his style. He doesn't deny God; he denies God in life, God's relevance, God's authority.
There are two ways to battle this aspect of Amalek. One is by forcing him to submit. Imposing God's will and declaring it to be superior to man's will. Place the human soul in a straight-jacket. This type of battle can be fought, and even won, but Amalek will still never be destroyed.
The second way to fight Amalek is to enlist him in the service of God. That fierce independence and unconquerable will, the creative drive of humans, can produce chiddush, creativity in the field of Torah. Ultimately, this will is itself Divine; there's no real conflict between God's will and man's; it's imagined by those who only look for God 'out there', and never bother looking 'in here'. Thus, it's the heir of Haman, the defeated Amalekite, whose traits are placed in the service of Torah, and whose contribution to the endeavor of Torah is immense.
There's a machloket acharonim as to whether the obligation to become inebriated on Purim is 'ad ve-ad bichlal' or 'ad ve-lo ad bichlal' - i.e., up to, but not including, the point where the division between Mordechai's goodness and Haman's evil becomes blurred, or even including that point.
The first position reflects the first way to combat Amalek, and distinctions between us and them must be maintained. The second ackn0owledges that, beyond a certain point, beyond good and evil, all is equally a manifestation of God's will, and even Haman can be a source of good.