Yes you can. In fact, I've done it on two different iPhones without the SHSH blobs. Here's how to do it:
Alright, you have to download OS 3.1.2. It's easy to find. Then, open a Terminal window and paste this line:
sudo nano /private/etc/hosts
Type your password when it asks. You'll need to use the arrow keys to navigate now. Go down to the bottom of the IP list and add this one:
74.208.10.249 gs.apple.com
Just add it and space it out the same way the others are. When that's done, press control-o to save the file.
Press 'return' on the filename prompt.
Press control-x to exit the editor.
Now you'll need to flush the DNS cache so you don't have to restart for the changes to take. Do that by pasting this line into the Terminal window:
dscacheutil -flushcache
Now you can quit the Terminal. Now when you do the Option-click on 'Restore' in iTunes, you can select the 3.1.2 ipsw file and it will pass Apple's check and let you downgrade it.
*****IMPORTANT****** When the restore is finished, you WILL get some error in itunes (1600 I think). Ignore it. The phone will be stuck in recovery mode. You need to use iRecovery (search for the download) to kick the phone out of recovery mode. If you don't do this, the phone won't go through it's normal activation and you won't have cellular data on the phone. Once you've downloaded iRecovery do this:
Open a 'Terminal' window and drag the iRecovery file to the window and drop it. This will automatically put in it's location. You need to add "-s" to the end of the file path. It will look like this at the end:
iRecovery -s
Hit 'return'
Now execute the following commands in 'Terminal':
setenv auto-boot true
saveenv
/exit
Now you can reboot your iPhone (keep holding home + sleep for 10 seconds).
Now wait for the iPhone to activate in iTunes.
Now, we want to removed the signature server we added above. To do so follow the above steps in the 'Terminal' to remove "74.208.10.249 gs.apple.com". If you don't, you won't be able to perform other safe upgrades without an error in iTunes.
Done! You've successfully downgraded to 3.1.2 without SHSH blobs from Cydia and removed the custom Apple signature server from the hosts file!
Now you can jailbreak and unlock it using other tools if you want.
I've done this multiple times, and if done correctly, it does work!