Depends on the state options really. If you're offered the local failing "crap" comp, then, 100% yes, it would be private. However if there is a good (in all ways) state comp that I could get my child into, then no.
My brother went to a private school in the 70s because he'd been allocated the local "sink school", and my parents scrimped and saved (driving a crappy old car, no holidays, etc) to pay for it, father was a shop manager, mother a secretary.
We'd have done the same for our son. But in the end, he was allocated into one of the best state schools in our catchment area and there was no need as he excelled, mostly because of little bullying, little disruption and little behaviour problems. It was a strict school and then suited our son.