mildly mathematical: can a planet be disconnected?

i had thought it final, that pluto is no longer classified as a planet .. but apparently the debate isn't over.

in particular, this article proposes to generalise the 2006 definition of "planet" as formalised by the iau, which according to the wiki, is a celestial body which:

1. is in orbit around the Sun,
2. has sufficient mass to assume hydrostatic equilibrium (a nearly round shape), and
3. has "cleared the neighbourhood" around its orbit, (meaning it has become gravitationally dominant, and there are no other bodies of comparable size other than its own satellites or those otherwise under its gravitational influence).

the novelty is in weakening the second condition: really, why should planets be round .. or even connected? the difference, to me, is whether we want the notion of a "planet" to be a geometric / topological one (i.e. dependent on shape) or a measure-theoretic one (or dependent on how mass is distributed).

having professed an affinity for gmt in past posts,
i suppose it's clear where my loyalties lie, this time.

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from "Not a Dwarf: Is Pluto a Binary Planet?" @discoverynews

".. that Pluto really has only four moons (all discovered by Hubble over the past seven years). He argued that the largest moon in the system, Charon (found in 1978), is really a planet in its own right.

Why? Because Charon is 12 percent the mass of Pluto. That may not seem like much, but our moon is only one percent the mass of Earth. Pluto's four other satellites are a very tiny fraction of the mass of the system.

The consequences are that Pluto and Charon pivot like a waltzing pair of ice skaters around a center of mass. So do the Earth and moon, but the center of mass, or barycenter, is inside Earth's radius.

However, alien astronomers watching Earth transiting the sun would note the passage of our moon as well. They might catalog Earth as a "double planet."

That was the reader's point. The four outer satellites don't really orbit Pluto; they follow strictly Keplerian orbits (the orbital period is directly related to orbit size) around the system's center of mass, which lies between Pluto and Charon. Pluto and Charon complete one pivot around each other every 6.3 days."
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this might be mathematically meaningful, but still seems like so much posturing. on the other hand, there's more to the second condition of hydrostatic equilibrium. again, the wiki:

Hydrostatic equilibrium or hydrostatic balance is the condition in fluid mechanics where a volume of a fluid is at rest or at constant velocity. This occurs when compression due to gravity is balanced by a pressure gradient force.

i claim no real understanding of physics, but this sounds like a stability property, in that the object under scrutiny has finalised its shape. it's just that typically, this forces the object to have a round one.

so for me, the jury's still out.

to prove that pluto is not a planet, someone has to convince me that pluto and charon are meant to collide and form a single, larger body, and that their current hydrostatic equilibria is just a transition before the chaos from that collision.