Yes, the Arkhalis is a reference to one of the rarest weapons in SotN with a very fast attack anination -- the Crissaegrim. And the Crissaegrim is dropped by a creature in the Inverted Castle called a "Schmoo", which is a ghost-like creature. Hence, the flavor text for the Arkhalis "I didn't get this off of a Schmoo..."
The Crissaegrim is slightly weaker than the strongest sword stat-wise, but it is one handed and the attack speed outpowers the stat-wise strongest sword.
So no, the Arkhalis is not a reference to the Master Sword, but the very slight chance out of a True Sword Shrine is a reference to how obscenely rare of a drop its imagined counterpart, the Crissaegrim, really is.
(It's also worth mentioning that the attack "blades" of the Arkhalis are a reference to the blades the Crissaegrim unleashes while attacking as well.)