Who can say. Depending on the tags you use, the file structure is changed and has to be rewritten. It is doubtful the Windows and Ubuntu negotiate the optimum way to minimize the data traffic. So assume the worst case.
But as every field modification in the file list invokes a write operation, it may be best to transfer the files for modification to the local storage, modify and then transfer it back.
One further note:
Even under the best conditions would network access currently run at 1 GB/s. Good local storages are far beyond this rate, so that any data transfer via the network must be slower than the local access. So while doing mass tagging, the network share would certainly be the sub-optimal solution.
Another scenario would be to have all the files as a local copy and then use a tool like "Synctoy" to transfer only the modifed files to the share.