No. They are born with a normal length tail (much like a Beagle). The breed has their tails docked as newborns (along with dew claws removed).
However our Jack's last litter she had a pup born with NO tail! We called her Fanny… because she was all fanny (rear end)… no tail. (I'm in the US – so it doesn't have the same connotation as in the UK)
There are many that are opting against docking the tail though and so will see some with long tails.Tags: jack russel terrier, jack russel