there is no question in my mind that capitalism could never have developed as it has without the state. and vice versa.
but when i think about this question in the current context, my mind goes directly to this:
what functions does the state provide that could not be provided by the "free market" and private enterprise?
muscle and protection of private property? nope, they've got that covered: private security, "police" forces and mercenary "armies" abound.
laws and regulations? the free market doesn't want 'em, they'd say "good riddance". or they'd "self regulate" - hahahahaha...
research and development? not a problem. sure, the capitalists would hate that there'd be no taxpayer money to massively subsidize the r&d that leads to their profitable products, but they'd figure that out. probably a bit less r&d is all.
centrally controlled currency? the fed is a privately owned enterprise already, if i am not mistaken. [edit: it is actually a complex combo of public and private. the fed banks themselves are private.]
the relationship between the state and capital is so tightly integrated that it is difficult to imagine one without the other. but if i approach it from the perspective of my (bolded) question above, i think there is some argument to be made that capitalism might be able to survive without the state. i just don't see it happening, and i surely don't see capitalists choosing to take on all the "responsibilities" that the state currently takes on (it would deeply cut their profits, and shift their objectives, for some period). but could they if they were forced to?
i am no economist, nor a political scientist, so my thoughts are not based on either area of theory; just observation of the world over the past 55 years.