Maybe. I always got the impression he was a United fan and was overjoyed to be the one making deals, like playing a game of Football Manager in real life. But, structurally, he should have realised sooner than a DoF was required. I also suspect that a lot of the signings were compromises with the managers rather than their preferences, and certainly the allocation of funds didn't always make sense, like signing off on a deal to sign Sanchez when at time LW was probably the last position we needed upgrading, Mata who didn't really fit into our formation and we were stocked with attackers. Di Maria and Lukaku who were marquee signings but both revealed being unhappy moving here. Signing of Lindelof was weird too, especially given the style of play under Jose. I actually sort of like Lindelof in a certain setup but he's the most un-Mourinho like CB you could imagine. Plenty more examples, but essentially, Woodward was taking on the DoF role, which is supposed to have broader strategical oversight over these things.
I think you make an important point though, I don't think any individual is really to blame, or we can say they were competent or not, because it's been a structural failing. Woodward will probably point to the scouting team and say well they recommended them, or point to the manager and say they OK'd them, or point to the commercial benefits of certain signings and say it was good for the growth of revenues, or he may say that other signings were vetoed by the Glazers. Likewise, I suspect the scouting team would say they were ignored over players X,Y and Z, and the manager may say he wasn't happy with the signings but when it's a choice between a player or nobody there's no option but to OK it. Individually, they may all have been competent, but ultimately as a structure it has failed, and the results have been as haphazard as the structure.