Your question itself assumes away quantum mechanics. There is fundamentally no fully certain particle in QM, the theory cannot meaningfully make predictions about something that's fully certain.
I've been out of school a while so might be wrong but maybe, just maybe, you could torture some mathematics into giving you some infinities if you really wanted to get a "prediction"?
But it's sort of like asking "how would linear algebra work if all nonzero matrices were invertible?" Well, all matrices aren't invertible, some definition of matrix that allows for nonzero matrices to be inverted is just different.
I think the more general question they're asking is whether it's possible to hack the math to break the uncertainty principle. As an example, if you take a Monte Carlo estimate of some quantity, you have uncertainty associated with that estimate. But there are ways to reduce that uncertainty using additional information (e.g. control variates, sampling tricks, partially solving the problem analytically, etc.). The example they're giving for a hypothetical particle with zero uncertainty might not be a great one, but I think the idea itself shouldn't be dismissed outright.
I think that misses the point of the exercise. What the OP is asking is more analogous to using negative energy in conjunction with existing models to see what would happen. It's not reflective of reality, but it tells you something about the limits of the model.
I've been out of school a while so might be wrong but maybe, just maybe, you could torture some mathematics into giving you some infinities if you really wanted to get a "prediction"?
But it's sort of like asking "how would linear algebra work if all nonzero matrices were invertible?" Well, all matrices aren't invertible, some definition of matrix that allows for nonzero matrices to be inverted is just different.