If the parent was born before his/her father was naturalized, then it's safe to say that the parent is not a citizen by descent; and if this parent "acquired it automatically...once the father has become Canadian by naturalization", then it's safe to say that this parent is not a citizen by birth. So probably the parent was naturalized at the same time with his/her father.
In conjunction with Seym's response, if the child is born in Canada, then his/her children will be Canadian citizens by descent if they are born outside of Canada (as the first generation born abroad). This would be the child's only 'privilege' for being born in Canada.
If the child is born outside of Canada (i.e. first generation born abroad), then his/her children will not be Canadian citizens if they are also born outside of Canada (as the second generation born abroad) because of the first generation limit enacted in the current Citizenship Act.