Probably not, Android itself needs a lot of RAM nowadays, and so do the apps. BlueStacks basically runs an Android layer on top of Windows, so it has the same drawbacks as Android.
Android 2.x runs okay on 256 MB RAM but anything newer will probably struggle to run at all on that little ram, and that's not even counting the apps. I don't think there is a BlueStacks version based on Android 2.x and even if there was, it would be old and probably not very good.
You can run Android 2.x in an emulator, that should somewhat work. If you install the Android SDK there's an emulator included which you could use, and there might be prepackaged images for VirtualBox or qemu or similar.