chip select on one to one spi connection
In general, it depends on the part. Some parts use the CS going high to process the data in the receive buffer.

Specifically for the Atmega168a in slave mode, yes, you can just ground the CS. However, you'll have no way to reset the SPI logic, so if you are off by one bit on one transaction that error will continue to propagate. 

So, it's possible, but not recommended. Especially if you're still attempting to debug the connection.