Normal “copy in” importing is safer for Audacity projects.
With the “faster” type of import, the audio data is not copied into the project, so the integrity of the project relies on the “source” files being available in the same location, with the same name, forever. The project depends on the availability of the original unmodified audio files.
Originally, the “faster” type import was even more unsafe than it is now. Originally, if you overwrote a file that had been imported, that would corrupt the project, because the project depends on the original unmodified file. This problem has been mitigated by creating an “-old” copy of the original file before overwriting the original.
That’s not the only problem with the “faster” import method. There’s also problems when trying to apply effects while the track has the blue stripes. Effects such as Amplify, Normalize, Compressor (and others) require that the file is fully loaded before the effect can be applied (these effects use the peak level in their calculations, and the peak level is not known until the import is complete).
Also, “faster” is not really faster at all, because the audio data will be copied at some point, it’s just a question of whether that happens at the time of importing or later. With modern SSD computers, the “faster” method does not even appear to be faster, because the time taken to calculate the waveform is much longer than the time to copy the data to a SSD.
The “faster” method will be removed from future versions of Audacity because it’s benefits are much less than originally expected (especially on modern hardware), and it’s disadvantages are greater. New versions of Audacity will however retain compatibility with old projects that have “dependencies”.
Audacity does warn you that it is going to overwrite the file before it does so, so I don’t think there’s anything inherently unsafe about that.
My advice would be to always use new and unique file names when exporting, so that you never overwrite existing files.