As anarchy is what we reach once the socialists have achieved their goal, it does seem possible that anarchy is an institution which underlies socialism.
But anarchists do not believe in institutions. The institution of believing that after the combination of all institutions which socialism tends towards, comes no institution at all.
Which is exactly the truth.
We have anarchy in front of us: the internet. The only organization it requires is the assignment of numbers.
Classless Inter-Domain Routing was introduced because classful routing made inefficient use of the four billion addresses that IPv4 gives us.
Network Address Translation was then introduced because DMZ's can be turned upside down and reduce the numbers that need to be assigned, significantly.
Linux Masquerading was the first example of this that some of us worked with: the gateway multitasked a masquerade.
It should be clear that there is little fear that the backbone of the internet be torn asunder by any other than the dissolution of all organizations.