I cannot explain what is happening on your machine, but I have just "recreated" the entire sequence on mine. I am using Chrome 47 on WIndows 10.
Once the Chrome PDF Viewer is disabled (and I've managed to turn off the "Always Open with System Viewer" option, which requires speed once it's on), the default action when click on a PDF link is saving the file.
After saving the file the pop-up menu on the downloaded file icon at the lower left presents: Open, Always Open with System Viewer, Open with System Viewer, Show in Folder, and Cancel (which is stippled out if the download is complete). This is confirmed in this post from April 2015 in the Google Product Help Forums for Chrome.
If I check the "Always Open with System Viewer" option all subsequent clicks on any PDF link cause it to open in whatever PDF viewer I have set up on my system as my default.
I have just repeated the process on my Windows 7 machine and it varies only in slight details. Adobe Reader XI is the default PDF viewer on this machine. After the Chrome PDF viewer is turned off the first click on a PDF link causes a save dialog to pop up and after the download is complete the standard split button for a completed download shows in the Chrome Status Bar at the bottom left. Clicking on the right side of the split button causes a pop-up menu to appear that has the following options, in order: Open when done, Always open in Adobe Reader, Pause, Show in folder, Cancel - none of which are stippled out. If I select the "Always open in Adobe Reader" option for this first file then all subsequent clicks on PDF links download the file "behind the scenes" and immediately open it in Adobe Reader.
There is no doubt that Chrome can and does do the same thing that Firefox and IE can do with PDF files. This may not be occurring for you, but it's not a feature lacking in Chrome, but an idiosyncrasy on your system.