I just did that the other day without flashing back to stock and I had no issues.
The issues people had in the past were caused by them updating their console with a dashboard that flashed their drive back to stock via a backup game disc. The first part of the update would complete, flashing their drive back to stock, then the 360 would reboot to do the second half of the update, but as the drive was now stock it could no longer read the backup disc in the drive to finish the update.
the only reason i would recommend is because i had a hitachi 59 that i updated with another drive because it was pre 13599, after the update i put the original back in that i had updated already to lt2.0, after the update of the console the system would not play any backups, it played all originals fine, but no backups. I cannot explain why that is, but i feel that if it had the original drive with original firmware i dont think i would have had the issue.
I ended up taking the lazy route and not flashing back to stock and just upgraded the dash via usb first. Luckily nothing erroneous occurred and my 360 is finally up to date and able to play some new games from the past few months. :)
