Of saving new FalloutNV.ESM: There were two duplicate groups which FNVEdit merges , aptly, with their originals.
[00:06] Background Loader: [FalloutNV_New.ESM] Warning: File contains duplicated top level group: GRUP Top "AMEF"[00:06] Background Loader: [FalloutNV_New.ESM] Merged 3 record from duplicated group: GRUP Top "AMEF"[00:06] Background Loader: [FalloutNV_New.ESM] Warning: File contains duplicated top level group: GRUP Top "RCPE"[00:06] Background Loader: [FalloutNV_New.ESM] Merged 1 record from duplicated group: GRUP Top "RCPE"
This, most likely, won't harm anything. If there were duplicate CELL or WRLD groups, this behavior could be problematic, but all other groups can be directly and safely edited by FNVEdit.
When FNVEdit fixes the above, a backup will be created. I'd suggest just keeping the backup handy, but playing with the fixed file.
If anything goes wrong, which I doubt it will, one can delete FalloutNV.ESM, then rename the backup to save time/skip Steam replacement.