Are carry flags set even when we discard the carry in an arithmetic logic unit?
This depends entirely on what the processor architects decided to do with the carry. Remember that the processor won't know whether a carry will or will not occur, and won't know whether the operands are signed or unsigned, so it just does the same thing whenever it does an addition.
Perhaps a better way to think about this is that there will always be a carry out of the MSB during addition. Sometimes the value of the carry will be 0 and sometimes it will be 1.