Hashem inspired me to respond as follows:
That's a good question. Chazal actually ask, "Where can we find Haman in the Torah?" And they answer, from the pasuk where Hashem asks Adam Harishon if he ate from the tree that he was commanded not to:
הֲמִן-הָעֵץ, אֲשֶׁר צִוִּיתִיךָ לְבִלְתִּי אֲכָל-מִמֶּנּוּ--אָכָלְתָּ?
What was the sin of Adam Harishon? Even though Adam and Chava had everything a person could dream of in Gan Eden, the Nachash convinced them that they weren't happy as long as they couldn't have that one forbidden fruit. They "took" for themselves something Hashem didn't want to give them, so-to-speak taking "control" of their own needs. (By the way, this is also what we do when we lust and feel "I need this", even though we know Hashem doesn't want us to have it and He knows what's best for us and He provides us with all our real needs.)
As a result of Adam's eating the forbidden fruit, it was decreed upon him that he would have to work for his food "by the sweat of his brow". This is a direct Midah Kineged Midah for his sin, as if to say, "If you don't trust me to care for all your needs and give you only the best for you, then go work for it yourself! No more "free-lunches".
Now let us consider, what was the root of Haman's great evil? Perhaps we can catch a glimpse of it from the Pesukim of the Megilah where Haman tells over to his wife and friends about his vast wealth, honor, and many children, and then he says: "And ALL THIS is not worth anything to me when I see Mordechai the Jew standing in the gate of the king!" Haman had enough to keep many men happy for many lifetimes, yet it's still wasn't enough for him if he didn't have EVERYTHING.
This is the same attitude that led to Adam Harishon's downfall! Perhaps that is why Hashem alluded to the future Haman when he berated Adam Harishon for having eaten from the forbidden fruit, since the attitudes of both came from the same place. (Maybe that's also why Haman was hung on "a tree", to allude that his demise was a step closer to the tikkun of Adam's original sin).
The Maan in the desert was a test, as it says in the Torah:
הִנְנִי מַמְטִיר לָכֶם לֶחֶם מִן הַשָּׁמָיִם וְיָצָא הָעָם וְלָקְטוּ דְּבַר יוֹם בְּיוֹמוֹ לְמַעַן אֲנַסֶּנּוּ הֲיֵלֵךְ בְּתוֹרָתִי אִם לֹא
The Maan came only once a day. Hashem was teaching us to rely completely on Him. As opposed to Gan Eden when there was enough sustenance forever, the Maan taught us to trust that Hashem cares for our needs precisely. Each day we get exactly what we need for that day, not a drop more and not a drop less.
Living on faith in the desert--one day at a time--was a test as well as a tikkun for the sin of Adam Harishon. And when we go to work each day to bring home food "by the sweat of our brow", yet we still trust that it is HASHEM who is providing for our needs (and not our hishtadlus), this is also a direct tikkun on the sin of Adam Harishon.
When we say Parshas Haman, we strive to increase our Emunah in Hashem's direct Hasgacha on providing us with all we need. Even though we don't have today the "Tzintzenes" of Maan that Hashem commanded them to put away for generations, we can remind ourselves of the lessons of the Maan by saying this precious Parsha, at minumum once a year (the Minhag is Tuesday of Parshas Beshalach). And by doing this and increasing our Emunah, we fix these faulty attitudes and bring the universe closer to perfection.
Again, it is the same with lust. Every time we see something that we know Hashem doesn't want us to have and we succeed in turning away with the trust that Hashem is providing us for all our needs and we needn't try to "wrest control" from Him by attempting to provide for ourselves that which He doesn't want us to have, this causes a tremendous tikkun in the upper words to the sin of Adam as well.
Tu-Bishvat falls out around the time of Parshas Haman (this year, it falls out on the Shabbos of Parshas Haman). Perhaps there is a connection between Tu-Bishvat, which is the Rosh Hashana of the trees, and Parshas Haman, where we increase our Emunah in Hashem's providing all our needs, in regards to the tikkun of Adam's sin with the Tree-of-Knowledge.
Ultimately, the sin of Adam Harishon will be fixed and Moshiach will arrive. The Koach of Haman and Amalek will be wiped off the earth and the world will return to a state where we will once again see clearly how Hashem provides us with everything we need. We will no longer feel a need for anything we aren't given by Hashem. We will be in state of shleimus - perfection.
So yes, Parnasa and Haman are directly connected :-)