I examined the file. You can edit that in an FCP SDR library using a Rec.709 project (which is what the Arri metadata shows), then export it as ProRes 4444. However, there are other metadata issues. These are not unique to Arri.
Cameras like Arri and even my team's Sony FX6s record lots of acquisition metadata which can be important in post production. This includes clip timecode and also many camera items. See below for an example from Arri.
The problem is exporting this from FCP (and I think other NLEs) does not carry over the original proprietary camera metadata to the exported file, even if the codec and container format is the same. Arri has a special metadata tool called ARRI Reference Tool which can extract this metadata from the camera files, but it cannot be inserted or merged into the NLE-exported file. The extracted metadata is apparently intended for use in specific post-production tools.
Another issues is clip (aka source) timecode. Even if adding an audio lane to otherwise non-edited camera files, FCP (and I think other NLEs) view that as a multiple timecode sources. E.g, the audio could have its own timecode so there would be conflicting timecode sources for the output file. The file is exported using 00:00-based timecode, not the original clip timecode. There is a third-party timecode tool called QTChange which lets you edit the timecode, and I think a batch operation is possible to read timecode from the original camera files and rewrite that to the newly-exported files. However, that would be an additional complex post production step that would require investigation and testing.
For these reasons (not because of color profile) I don't think it's feasible to add audio to the Arri clips without losing important metadata. If you don't need the metadata (now or in the future) you could go ahead and do it, but I would discuss that in advance with the assistant editor, post-production supervisor, or whoever has that responsibility.
Arri ProRes metadata sample:
Media/UUID : BB3B0738-7A72-11EF-85D9-000E8E6ED4DB
com.arri.camera.CameraId : A20D
com.arri.camera.CameraIndex : A
com.arri.camera.CameraModel : ARRI ALEXA Mini
com.arri.camera.CameraSerialNumber : 22605
com.arri.camera.ColorGammaSxS : LOG-C
com.arri.camera.ExposureIndexAsa : 800
com.arri.camera.LookFileBurnedIn : No
com.arri.camera.NdFilterDensity : 1200
com.arri.camera.NdFilterType : 3
com.arri.camera.ProjectFps : 24000
com.arri.camera.ReelName : A001A20D
com.arri.camera.SensorFps : 24000
com.arri.camera.ShutterAngle : 1728
com.arri.camera.SupVersion : 6.01.02
com.arri.camera.SxsSerialNumber : 224003201294
com.arri.camera.UserDate : 20240924
com.arri.camera.UserTime : 12h44m25
com.arri.camera.WhiteBalanceKelvin : 5600
com.arri.camera.WhiteBalanceTintCc : 0
com.arri.camera.CameraClipName : A001C025_240924_A20D.mov
Color primaries : BT.709
Transfer characteristics : BT.709
Matrix coefficients : BT.709
Time code of first frame : 03:47:08:15
Time code of last frame : 03:47:22:22