The reference linked in the OP says:
With the full amount spent on the F-35 at its disposal, the U.S. could afford to purchase every person on the streets a $664,000 home.
the reference states:
On any given night in 2013, the Department of Housing and Urban Development concluded, there were an estimated 600,000 homeless Americans living on the streets.
The reference states that:
current acquisition price-tag of $398.6 billion
$398.6 billion divided by 600,000 = $664,333
So it is clear that the reference is arriving at the statement "the U.S. could afford to purchase every person on the streets a $664,000 home" by dividing the total acquisition cost by the estimated number of homeless people.
The flaw in the statement is the $398.6 billion is not money that has been spent. Instead, this is the money expected to be spent through 2037. As explained in the Reuters article Pentagon needs $12.6 billion per year through 2037 for F-35:
the Pentagon was expected to shell out $316 billion through 2037 on the remaining development and purchase of the radar-evading warplane, on top of billions of dollars already spent, for a total program cost of around $400 billion
So, the fact that only $84 billion (not $398.6 billion ) has been spent so far makes the value $664,000 (or $600,000) be an exaggeration.
In summary, that fact that the OP is written in past tense terms ("vast amounts spent on the airplane so far", "money spent" and "could have been given a $600,000 home") but then uses future spending through 2037 to arrive at the $600,000 figure, makes the claim in the OP false.