Lewa might not have adapted quite as quickly as needed for that last season, but longer-term, yeah, I think the only half-rigorous argument about it - assuming that he didn't suffer the Bundesliga disease' that seems to particularly ail many of their signings in adapting to the league (which I think is an unlikely scenario, given his quality and attributes by 2013) - is an 'accelerationist' one. I.e. he might have papered over the cracks even more than already happened. And even that's probably a dubious line of reasoning, since we'd end up at the same place, maybe just with another trophy or two (another FA Cup, the EL, if we'd still failed to qualify for CL the previous season)...
It's frustrating to think more broadly though how many of these players we could have signed and were seriously in the conversation to sign, even with the Glazers, to the point where provisional deals were agreed or fees agreed that the club ended up spending elsewhere on (at least borderline) duds. That same transfer window, we could have signed Mousa Dembele for the same price as Kagawa - add to Thiago the following Summer (lined up by SAF, if dithery Moyes hadn't stalled and eventually allowed Bayern to step in) and Kroos the next Summer, and that's a midfield that carries through to the next 3 seasons once together and solves short-term issues. Other., far 'less suitable players were bought those same summers for same prices or more.
Likewise with united fan Fabinho, being offered to the club and quoted at a price slightly less than Matic ended up being and who could have replaced or alternated with Dembele by that point, Mane instead of De Pay, then Haaland when at Molde and Ole (pre-appointment) recommending him as one of the best young strikers he'd ever seen and the club lining up a deal before they screwed it and allowed Leipzig to finalize...