No they are not, I'm surprised people think this.
https://www.thefa.com/news/2025/feb/28/emirates-fa-cup-quarter-final-draw-details-20252802
They are numbered by the number of the draw from the last round. This is why people say we would've got x in this round.
It's only in round 1 and round 3 that happens with the teams coming into the draw.