I can confirm that this method worked to root BB 345.
Edit:
nandroid backup hangs at "Backing up firstboot. . . "
Here is exactly what I did to my phone:
Updating to baseband 345, Android 2.2.2 and then rooting phone.
Starting point - rooted, carrier unlocked Streak with baseband 318 with the performance fix and Streakmod recovery installed
Backup apps/data with whatever means you prefer
power off phone
start streakdroid recovery
- wipe cache partition
- wipe dalvik cache
- make a full nandroid backup
- mount sd card via usb
-- copy superuser.zip to sd card
-- copy the update.pkg file for 345 to sd card
- unmount sd card
reboot phone into fastboot mode
flash the recovery.img for 345 to the phone
reboot to the stock recovery ( at this point I disconnected the usb cable)
install BB 345 via the stock recovery option 2
Let the phone reboot - this may take a few minutes for first boot, be patient.
- at this point I did the setup, entering my gmail account.
power off
start phone in fastboot mode
flash streakdroid recovery to the phone
reboot into streakdroid recovery (do not let the phone boot normally as the recovery will be overwritten)
install the superuser.zip file using streakdroid recovery
reboot phone
- superuser app is now in app tray
went to market and installed Titanium Backup and Busybox installer
confirmed that device was rooted
powered off and started in recovery mode, stock recovery had replaced streakmod recovery (so you can just go ahead and do what I did next and skip this

)
installed root explorer and renamed install-recovery.sh to install-recovery.sh.orig (the file is in /etc)
powered off phone and started in fastboot mode
flashed streakmod recovery
reboot phone
shut down and start in recovery mode - confirmed that streakmod recovery is working
- attempted do a full nandroid backup, hangs up at "Backing up firstboot. . ."
- reboot phone and customize as desired
Now that I have this rooted I will play with it for a few days.
Never ask before searching!
Current Device: AT&T LG Optimus G, stock, rooted JB
Retired Devices: At&T Galaxy Skyrocket, Dell Venue, Dell Streak, Moto Flipside, Moto Backflip, Samsung Eternity