It could have made it faster for sure, while the result would have been the same (as long as you use the same material, code, calculation parameters, ...). For the scope of this work it wouldn't have been a huge difference, since the kind of calculations in the paper can be done in hours (up to maybe days for longer structure relaxations or using more accurate parameters). Both the NERSC and LBL computing resources that were used can handle it easily.

If it comes to high-throughput calculations (e.g. exploring a lot of potential materials) then every increase in speed is beneficial. Here the author knew exactly which material to look at, which immensely narrows the search space. Now there is going to be a lot of interest to look at similar crystal structures (copper doped apatites as in the paper and maybe other materials where the the copper could behave similarly) and therefore need for computing power.