With DS1, I'd never heard of flat-head or plagiocephaly, and he slept brilliantly on his back all night from a young age, and spent hours each day lying flat on his back on a playmat / under a baby gym because he seemed so happy doing that. His head is absolutely perfect, never developed a flat spot at all, even though he would have spent literally hours lying on a (fairly non padded) playmat on the carpet.
With DS2, the HV pointed out that his head looked quite flat across the back at the 8 week check, and advised all the corrective measures (tummy time, repositioning etc). We did all this, bought the Clevamama pillow, limited time on his back during the day and never used the thin playmat etc, and his head shape did improve as time went on although it never totally righted itself. Crucially his eye and ear alignment was never affected so we didn't go down the helmet route. You wouldn't notice it now (3.5) but if you place your palm against the crown of his head you still feel a flattish bit there.
Having experienced flat head with DS2, we were soooo careful with DS3 (now 3m), but despite all our efforts (and the fact that DS3 has spent more time in a sling than both the others put together) he too has developed a bit of a flat head across the back. I am being careful re time spent on his back during the day, and he has the Clevamama pillow in his cot for nap and bedtime time; the problem is though that these pillows do not fit into the moses basket and of course in the early weeks/months that is generally where he's spent the night which I think was where the flat head developed. Again, though, there is no impact on his eye/ear alignment so I don't plan to go down the helmet route. I am a bit paranoid about it though and am definitely keeping a careful eye...
So my conclusion would definitely be that it depends on the individual baby!
I would say try all the corrective stuff, and bear the helmet in mind as a possible option in the future. As others have said it doesn't affect brain development at all but I have heard of concerns around overheating at night when wearing it (a friend whose LO had a helmet was told to only dress him very lightly at nighttime as his overall body temp would be higher whilst wearing the helmet) so that is something to bear in mind too.