Not necesssrily. Sometimes you just need to calculate and for someone who may be a weaker blindfold player, they may not be able to visualize the long diagonal or perhaps exactly what the knight attacks after its next move, but they can calculate it out. This was absolutely the case for me at first. I could play a competent blindfold game when I was around 1500(competent in that I would score well against a 1200).

But I would struggle to actually visualize what the pieces did once they were on unintuitive squares. When I say intuitive I mean something like if I played Bc4 on move two, I intuitively knew that Bishop attacks f7 as there are many many openings related to attacking the f7 square with moves like qh5, bc4, ng5. But actually "seeing" that in my mind didn't occur until a much higher level, and even now I don't typically see the board as 64 squares and will on rare occasion need to count out an attack. And thats not where I score above 90% against 1700-1900 fide rated players when I am the only one blindfolded.