I'm not sure where such a team would find supporters, but I learn through a tweet (that at first went over my head) that they, like the Lions team, have been named after one of the supporters in the royal arms of the United Kingdom.
Making up the numbers, I doubt they're expected to win much. Indeed,
The lion and the unicorn
Were fighting for the crown
The lion beat the unicorn
All around the town.
What's surprising is that an English team has been given that name. Surely someone in the ECB knows that the unicorn is the Scottish counterpart to England's lion?
Of course, according to Lewis Carroll's White King, even the winner does not get the crown, but the nursery rhyme continues
Some gave them white bread,
And some gave them brown;
Some gave them plum cake
and drummed them out of town.
and Alice does give the lion twice as much plum-cake!