In the PIC environment, making a pin an analog input disables the input buffer, so the setting of a weak pull-up is mooted.
However, it appears that atmel don't follow the same strategy because there is a warning that setting weak pull-up on a pin set for analog input will affect the values reported by analogread.
I would recommend a deep read of the datasheet(s). I have read the datasheet again, and while I can see that the pull-up can be functional on an analog input pin, I didn't find the warning. However I did find people using this feature to read light levels using an LDR (where the weak pull-up forms the upper part of a voltage divider).
Note that this doesn't detract from anything
@dorke has said. However, it also doesn't mean that you can't think up a situation in which this pull-up could be used for some purpose in conjunction with analogread.