Can I use PIR + HC-06 Bluetooth Module without arduino to send events to Android?
Not with the HC-06. The HC-06 is a specialized firmware for the CSR bluetooth module it runs on. It lacks any options for GPIO, either from a master or to it.

There are other versions. The HC-05 is even more limited. A newer version known as the BC-04C or some variation on that now has a limited GPIO option, and can be run without a microcontroller host hooked up. (Electrodragon, not affiliated), but it has poor documentation.

See https://www.youtube.com/watch?v=ExtMyV3fDLM or https://www.youtube.com/watch?v=KMUMnF0F4jE 

Even so, you would need to setup the module at least once, with a microcontroller or a usb-to-ttl serial cable, and put it in Monitor/Collection work mode (input reading mode).

As for directly hooking up the PIR output to the TX pin, that can create garbage characters that might lock up the module. I don't recommend it.

The easiest solution would be to use an Arduino clone, or ATTINY and make a quick sketch that involves reading an input pin, and sending a string via the TX and RX pins (software serial). It wouldn't take much.

Edit: A simple hack would be to use a device like a Bluetooth Selfie Stick button. These buttons are a fully contained bluetooth with multiple digital inputs, and even a battery. Add a transistor and a resistor and your all done. There are apps that can configure what the button "press" does on the android side. I may do this myself now!