Considerations when using internal pull-up/down resistors
Yes... You can... It's a proven feature.
If you see pin structure in STM32 Reference manual, you can see that it has required components  --



If this satisfies your requirements, then, you can do away with external components. 

Edit  Remember that at Power up, Pins will be tristated. If it does not hamper your application, it is good! That's why it's good practise to init IO section first and then go ahead with other peripherals.