I do not believe there is an extension that will keep your tab from changing the URL, pinned or otherwise.

Update:

I've worked on a more complete solution based on the script below. It is called FEleven and it is hosted on GitHub: https://github.com/iglvzx/FEleven

One of the main benefits of FEleven over the the solution below is that I've included built-in support for Google Chrome and other browsers, allowing you to omit the window-title parameter, i.e.:

feleven "path\to\chrome.exe ..."

If only there was a way to automatically press F11 once Google Chrome was open...

There is! With a little help from AutoHotkey we can launch Google Chrome in fullscreen mode. Now, F11 is pretty standard as a fullscreen keyboard shortcut, so we will write a script that can work with any program we throw at it! Let's begin...

1. Setup

So, one little known feature about AutoHotkey is that you can call scripts from the command line (and with parameters). We will be compiling the following script; I named mine Fullscreen.exe.

#SingleInstance, Force
#NoTrayIcon
SetTitleMatchMode, RegEx

Title = %1%
Title := Title . "$"
Target = %2%

Run, %Target%

WinWaitActive, %Title%
Send, {F11}

ExitApp

If instead you would like to maximize the window instead of pressing F11, replace Send, {F11} above with:

Send, !{Space}
Send, x

Outline:

1. Launch the Target

2. Once we have an active window whose title ends with our Title, send F11 to enable fullscreen mode.

Note: If don't want to install AutoHotkey or compile your own script, I have uploaded a compiled script for you on my server:
ahk.igalvez.net/Fullscreen.exe, 772 KB

Alternative for maximizing the window:
ahk.igalvez.net/Maximize.exe, 772 KB

Demonstration:

Now, you can launch an application in fullscreen by calling the .exe like so:

Fullscreen "Title" "Target"

Assuming that you are currently in the directory where Fullscreen.exe is located, or Fullscreen.exe is in a %Path% directory.

Example:

Fullscreen "- Google Chrome" "%LocalAppData%\Google\Chrome\Application\chrome.exe"

Use it in shortcut (.lnk) or a batch (.bat) file!