Hey
unfortunately this will not help you. Bluestacks is a virtual machine that sits on top of your operating system and has no real direct access to hardware. All access is via software, so as soon as the laptop is formatted bluestacks is gone.
However if you have one of the few rare laptops with built in GPS, Lojack and other solutions you may be able to recover it. Hoping your laptop was covered under home insurance or work insurance in which case pay your deductible and move on.
I have found that a few things do help with such issues.
1. Get some secure cloud storage - This makes sure if you lose your laptop your documents are intact. Dropbox gives away 50Gb for two years free if you purchase certain android phones. The nice thing about drop box is if you lose your machine, deauthorize it. Better still use two step authentication to have it verify by sms each time you login.
2. Regular back ups.
3. Identifying marks can help recover your laptop. Everytime you drop it, ding it, scratch it etc make a note.
4. Get the invisible ink markings on your device.
5. Try your luck with the authorities. Its hit and miss but they have recovered many a laptop at Ximex etc.
all the best
