It is possible to use EndNote to place citations into a Google Doc. It will take a few steps and you will still need to have EndNote installed on your desktop.
Step 1: Drag and drop your citations from EndNote to where you want to place them in your Google doc.
Step 2: When you're finished writing, download your Google doc in Rich Text Format (.rtf)
Step 3: In EndNote, select Tools - Format Paper - Format Paper and choose your .rtf file
Step 4: In the Format Paper dialog box that appears, choose the citation style you want under Output Style and click Format.
Step 5. Save the paper as an .rtf file to your desktop. Note: you will lose the citation formatting if you upload this file back into Google docs so complete these steps after you're finished writing.