Can the Arduino Eclipse plugin use the libraries installed by the Arduino IDE?
I fear that what you want is not 100% possible.
For libraries I am 100% sure it will work but the problem is the platforms.
UPDATE arduino IDE (no longer)? decompresses libraries and as such the libraries are unusable in Sloeber.    

Lets start with the Libraries
What you do is:
In arduino eclipse ide remove all libraries from the library manager.  

In windows->preferences->arduino->"private libraries path" add the libraries folder in the arduino IDE install and add the libraries folder in the arduino15 folder maintained by the library manager.
It is important to point to the parent folder containing the libraries. All subfolders are assumed to be libraries.  

Then the boards
The problem here is that the boardsmanager adds environment variables to link boards to tools. You may have read remarks about A.RUNTIME.TOOLS.AVR-GCC.PATH and A.RUNTIME.TOOLS.AVRDUDE.PATH not being defined. Well it is the boardsmanager that maintains these based on json file content.
If you can limit yourself to 1 version of AVR, SAM, AVRDUDE, BSON,... tool chain you can "make it work" as follows:
Step 1: Keep as little boards as possible installed. You have to keep at least 1 or the plugin will reinstall the AVR boards of Arduino when started.
Step 2: In windows->preferences->arduino->"private hardware path" add the hardware folder in the arduino IDE install and add the packages folder in the arduino15 folder maintained by the Arduino IDE boards manager.
Step 3: Recreate the project in eclipse as described in your other question.
Step 4: If the build fails modify the [eclipse installation]/arduinoPlugin/post and pre processing files to try to get it to work.
Step 5: in project properties->Arduino select apply and OK (this will take your changes in step 4 into account)
Step 6: Goto Step 4

Good luck
Jantje