Yes, it can. Is it in this instance? The claim is that there is nothing to discuss.
Look at it this way. I assume your car in in metric units. Go ahead and try to strap on a bunch of imperial unit engine parts to your car. Not going to be easy, and not worth the expense. Better to just stick to metric, and wait until you build a car with a small block Chevy engine before going to imperial.
In this case it's a new program, but they are reusing shuttle parts in imperial. Is it worth redoing all of that old work? I don't know the answer to that, and no matter how many pages this thread gets to, I don't think we can armchair quarterback this. But if they can't get the money from Congress, the decision is pretty stark - stay with imperial, and get the project done, or just cancel the project. Yes, perhaps a cost study would show that in the long term sticking with imperial would cost, say, $1B over the life of the program. But if you don't have the money, you don't have the money.
Engineers face these kinds of decisions every day. I'm a software engineer. When dealing with old code, it's always substandard. The question is: revise, replace, or deal. More often than not, the decision is to just deal. Almost all technology in the military is obsolete in one form or another (don't nitpick with all the obvious counterexamples please). It's a necessity due to long lead times, extensive testing, etc. Wasn't the shuttle flying with core memory? It's the kind of thing to drive you crazy, but you can't just buy a modern PC and slap it in there - that little decision, easy to do in the commercial space, means hundreds of millions of dollars in rewriting code, retesting things, etc. So, you deal.
Naturally, it would have been nice for NASA to switch to metric for a new program - a perfect time to do so. But they are reusing old technology, and so it becomes an issue. Rework the old proven technology (never a perfectly safe thing to do), stick with the old units, or use a frankenstein approach of some imperial, some metric. We already have examples of failure when you mix units like that. None of the decisions are easy. I wouldn't want to be the guy in charge of making this decision. No matter which decision you make there are failure paths, and you are going to be criticized and second guessed. I applaud the decision to not go with the politically expedient decision. Was it the "right" decision? Who knows? I think it is beyond anyone's knowledge to really say, even the decision maker's. But in this case what was the alternative? Shut down the program, or introduce unknown risks for the life fo the program by mixing units.