For quick reference for those needing help with their BitDefender, or a general direction with AV issues at all.
RESOLVED. Thank you CW! This did help confirm the issue... BitDefender has not been generating any notifications or quarantining any items, so this has made finding the fix a little bit annoying, but not impossible:
Root Cause: BitDefender was blocking the creation of ParagonChatClient.exe in the %appdata%\ParagonChat\Bin folder, when launching the %appdata%\ParagonChat\Bin\ParagonChat.exe updater.
Fix/Workaround: These general guidelines apply to AV (antivirus) applications in general. BitDefender (specifically, BitDefender Total Security 2016) specific steps marked in blue text for each step.
NOTE! %appdata% refers to your AppData folder, and may vary depending on your installation of Windows... Make note: it is a HIDDEN folder so will not show on an explorer window by default.
If in doubt, type %appdata% and hit enter, and it should bring it up for you... For Windows 10 64bit for example, this will be: C:\Users\<your Windows logon name>\appdata\Roaming\
With that said...
1) BACK UP YOUR DATABASE TO A SAFE LOCATION!
Navigate to %appdata%\Paragon Chat\Database (note the SPACE in Paragon_Chat) and copy the ParagonChat.db file to your desktop for example... The new Paragon Chat uses some copy/move mechanics, so it's strongly recommended you keep a VERIFIED WORKING copy of your DB somewhere completely removed from this entire procedure...
2) REBOOT COMPUTER
This is to clear out any session-based threat monitoring your AV might be holding onto; ie specific, recently detected processes, folders, etc...
3) DISABLE ANTIVIRUS APPLICATION
Depending on which AV you use, this process will vary. MAKE SURE ON-ACCESS/ON-READ/ON-WRITE SCANNING IS DISABLED.
a) Double-click the "B" icon in your task bar to open the BitDefender console.
b) Click 'Modules' at the bottom of the BitDefender console.
c) Click the little gear next to 'Antivirus' to open its controls.
d) For 'On-access scanning' click the slider on the right side of the screen so it shows a grey 'X' instead of a blue '✓' and choose how ever long you'll need to leave it disabled for; I recommend 15min or 30min.
e) For 'Active Threat Control' do the same thing; click the slider box to its right to get a grey 'X' instead of a blue '✓'
4) RUN\INSTALL NEW PARAGON CHAT
If you already updated to the 1.0.0 launcher, then you should just need to run Paragon Chat (ParagonChat.exe in %appdata%\ParagonChat\Bin)... This should proceed without incident or error notification.
Once the Paragon Chat launcher is in a ready state (green bar at the bottom, and you are able to enter your credentials and click 'Log In'), CLOSE Paragon Chat.
5) ADD FILE/FOLDER EXCEPTIONS AND ENABLE ANTIVIRUS
There are three, specific items you want to add exceptions from both ON-DEMAND and ON-ACCESS/ON-READ/ON-WRITE scanning for:
Folder: %appdata%\ParagonChat
File: %appdata%\ParagonChat\Bin\ParagonChat.exe
File: %appdata%\ParagonChat\Bin\ParagonChatClient.exe
YES, you DO want to add exceptions for ALL OF THESE. Excluding the ParagonChat folder implies it will exclude the executables in Bin, but it won't from my experience. Explicitly add them for exclusion as stated! And as stated in the note, %appdata% is basically a shortcut/shorthand reference to the appdata folder... Typically c:\Users\<your user name>\appdata\roaming
Once your AV exclusions are set, enable your antivirus again to stay protected from actual threats. 
ADD EXCLUSIONS
a) In the same place you disabled your antivirus functions, click the 'Exclusions' tab, between 'Shield' and 'quarantine' toward the top of the Antivirus window.
b) Ensure 'Exclusions for files' is enabled, by clicking the slider to its right; make sure it shows a blue '✓'
c) Click on 'Exclude files and folders'
d) Click the 'Add' button
e) Make sure the radio button is set to 'Both' and click 'Browse'
f) Use the +/- signs to find the ParagonChat folder... AGAIN, REFER TO THE NOTE FOR WHERE THIS IS!
g) Select the ParagonChat folder, and click OK
h) REPEAT steps 'c' through 'f' to get inside the Bin folder in the ParagonChat folder...
i) Select ParagonChat.exe, and click OK
j) REPEAT step 'h'
k) Select ParagonChatClient.exe, and click OK
*Your exclusions list should now show these three entries, similar to this.
RE-ENABLE ANTIVIRUS
l) Click on the 'Shield' tab to get back to your Antivirus settings.
m) Re-enable 'On-access scanning' and 'Active Threat Control' by clicking the slider to the right of each, so you get a blue '✓' instead of a grey 'x'
6) LAUNCH PARAGON CHAT
It should launch fine, generating no errors and allowing you to log in and play the game... Voila. Done.
I hope this helps some folks out there!
