Is a QR Code still readable when some areas of are damaged or missing?

It depends on the Error Correction Level
In general, yes. It depends on the error correction level, that is being set when creating a QR Code. Error correction ensures that the QR Code stays readable, even if the QR Code is partially damaged, covered or pixels are missing.
There are 4 different levels:
- Level L - up to 7%
- Level M - up to 15%
- Level Q - bis 25%
- Level H - up to 30% of the QR Code may be damaged to stay readable
The higher the error correction, the more the QR code can be missing/damaged, but the bigger is the size of the QR Code.
Recommended Error Correction Level
If you just have a black & white QR Code, the error correction level L is sufficient.
We recommend to always use the highest error correction level H for designer QR Codes, so you can maximize the size of your logo in the QR Code.