I know this is an older thread, but one solution I have enjoyed is just setting the default application to open PDF files in Windows to Chrome.
Control Panel > Folder Options > File Types > Scroll down to Extension "PDF" > Click "Change" > Click "Select Application From A List" > Select "Google Chrome"
Now, conceivably, once you got to the PDF Extension in the File Types tab, you could click Advanced, then click Edit "open" action (or Create, if the "open" action doesn't exist) and in "Application used to perform action" field, put " --focus-on-existing-tab-on-open=false %1"
This way, if you don't have Chrome running, but you have a bunch of existing tabs when it does come up, it doesn't replace an existing tab, but rather opens the PDF in another new tab.
Hope that helps.