Nothing ever gives guarantees. If the question is changed to do Cat One Academies produce more top players than other academies? the answer is obvious.
Nobody would argue that investing less in the transfer market will, on average, yield lesser quality players either. The positive correlation is obvious. This is a similar thing.
That said there's a trade off. United do have a successful system within a lower cost model. There was a dormant period pre DCL/Ramsdale and changes were made then. Quite a bit was made of it in the media and people were talking about it being a waste of money on here. It has been successful since then, certainly amongst Cat Two systems. A bit of an outlier.
I suppose the trade off is "will the extra money be more useful there than spent in the transfer market?" The productivity levels will determine that. Personally I'd also question how sustainable the current productivity levels are within a Cat Two system (see "outlier"). I don't think current success levels can be taken for granted within a Cat Two framework.
Ownership is a consideration. If United ever get ambitious owners then the SCMP/FFP advantages of the higher productivity levels likely under Cat one are obvious. The benefits to the accounts which allow a higher level of investment in the first team in the transfer market are there for all to see. It's one method of legalised financial doping within the game. Sell an academy player or progress one to the first team and you benefit enormously account wise, as they cost nothing initially.
Another factor is facilities. You can build the facilities without having the Cat one status. Then you can move within categorisations depending on the current financial situation of the club. The facilities aren't there and you are locked into a lower categorisation. It's possible to support big academy investment without necessarily supporting a move to Cat One. If a great site was on the market suitable for Cat One specs United should get it, imo, even if we remain Cat Two.