No, this isn't a feature in FormsCentral. Each submission gets a date/time stamp, the first column in the response table. Other than that there is no automated unique ID you can set.
Depends how many responses you anticipate, I therefore realise not ideal, a workaround I have used is;
Import responses into Excel.
The Date / Time field, whilst displayed as Date and Time, is in fact encoded.
By re formatting that column in Excel to, for instance, 'Number' (with no decimal places), you get a code for the day.
If you format, with decimal places, you get the time code as well. The more decimal places you allow, the more unique (is that English?), the code.
Just a thought