Straight from Disc
You can play .hack//fragment on a Playstation 3, but there are a few caveats. The Playstation 3 is region free when it comes to playing PS3 disc based games. However, the PS2 backwards compatibility will only play PS2 region discs based on your PS3's region, i.e. a North American PS3 can play NTSC-U/C Playstation 2 disc based games; and a Japanese PS3 can play NTSC-J Playstation 2 disc based games.
Only the original fat PS3 model CECH-Axx is fully backwards compatible with PS2 disc based games whereas original fat PS3 models CECH-Bxx, CECH-Cxx, CECH-Exx use software emulation. All later models do not have any form of backwards compatibility packaged in.
So if you wanted to play straight from the .hack//fragment PS2 game disc, you can do so on a Japan region PS3. A Playstation 3 Test Debugging model is region free when it comes to it's PS2 game discs, so this is an alternative option to playing straight from the disc. You can play .hack//fragment on a Playstation 3 in OFFLINE mode on a NSTC-J Playstation 3 and on a NTSC-U Playstation 3 Test Debugging console straight from disc.
But let's say you want to play in ONLINE mode from the disc, the game disc still points to the defunct Bandai Network's IP address j5q.channel.or.jp which is no longer in service and you need the game to point to a.dothackers.org. To do so, on a NTSC-J PS3 or a NTSC-U PS3 Test/Debug model, you will need to do a DNS redirect to 18.104.22.168 (thanks 1UP).
From an Disc Image
To do so, you will need to install on your retail PS3 a custom firmware. A retail PS3 does not allow you to copy/paste an ISO disc image onto your PS3 hard drive or USB flash drive and play from the disc image. Installing a CFW or custom firmware such as Rebug, Ferrox, and others will enable to use Multiman to launch games. This will allow you to play .hack//fragment in OFFLINE mode, and if you have a backwards compatible PS3 such as CECH-Axx, you will have the option to playing in ONLINE mode. Just make sure you patch your .hack//fragment disc with Telipatcher, which will add the proper lobby server IP address. Later PS3 models such as the Slim and Super Slim, will not have the option to play in ONLINE mode.