Yes for a fixed amount of effort the more you dedicate to formalization the less room there is for exploration. So the constraint is the total budget. The other constraint is if your language doesn't have the concept of gravity it is less likely you are developing the theory of gravity. So if you want to talk about modularity lifting in Lean you need to build up theories on elliptic curves, modular forms, modular curves etc first, because the library doesn't have them even if you consider them elementary. So now if you have a Lean proof with little effort I can infer that it is unlikely to say anything deep about these subjects. If you only have a paper proof, otoh, that doesn't bound your distance from the basics for me.
Would I be correct in saying that you're making a claim about how difficult the statement is to prove, rather than the accuracy of the proof?