Right- dumping to a DAW saftware (Cubase or whatever) via the ADAT ports on the sourdcard will simply create the files on the machine in whatever the native format needs to be. No conversion there: it's all native from the word go.
You can record a session on the Fostex, perhaps working remotely. Then, when you get it back to your DAW, you can plug in via lightpipe and rerecord the data on the DAW (playback on the Fostex, record on the DAW). Since your audio data will be going over in PCM digital form, there's no reconversion: it's just a bit-for-bit transfer. You can then dump the files that are created by the DAW software to tape, CDROM, external SCSI device, or whatever format you prefer for backup.
That's the way I got started with my DAW. I bought the 1624 first, since I'm an old analog guy and just wanted something that acted like a simple old 16-track tape machine (and didn't involve PCs or Windows at all!). Later, to do backup, I built the DAW so that I could fly the tracks over, and then back up to my tape machine via Ethernet from the DAW. Only after doing that for a while did I finally come to (grudgingly) admit that the DAW is better for certain types of things (MIDI-based music, extensive editing, unusual plugin-based processing).
I still track primarily to the D1624, and consider it to have been the best single purchase I made. It *never* lets me down, which is something I cannot say for Cubase on my DAW. I do not want to lose takes to crashes, setup errors, or other computerlike annoyances. The 1624 is always ready, and it really does act just like a simple, basic, analog 16-track tape deck: arm the channels, punch "record", and you're printing tracks without question.
DAW software has a host of hazards that can cause crashes, or recording dropouts, or annoyances. There are a huge number of different ways that you can have recording problems with a DAW, basically- especially in the heat of battle, when the talent is in the room and the juices are flowing. A DAW is unquestionably much more powerful than the Fostex, and much more versatile: but with that versatility comes the very real threat of annoyance and interruption of the creative flow. I personally prefer to get the tracks while the fingers are working, and *then* transfer to DAW at my leisure for editing, munging, and such.
There's nothing more frustrating than doing an overdub in Cubase, and realizing after you've finished it that you forgot to move the "right marker" out past the end of the tune. so Cubase did what you told it to, and quit recording at the right marker: 2 seconds into the perfect take. When I'm recording, I want there to be _zero_ chance of losing a good take due to my own foolishness, or being in a hurry: so I use the right tool for the job.