What happens if you Apparate correctly without a license? Is there any way to detect Apparitions without licenses as there are to detect Underage magic?
There can't be any way to detect Apparition without a license.
For the simple reason that Harry successfully Apparated multiple times in HP and the Deathly Hallows without a license: he was too young to get one when Ron and Hermione did their tests. In fact, he even Apparated undetected in HP and the Half-Blood Prince, when taking a weakened Dumbledore from the sea cave back to Hogwarts.
But if you do get caught doing so, you get fined.
"You have to pass a test to Apparate?" Harry asked.
"Oh yes," said Mr Weasley, tucking the tickets safely into the back pocket of his jeans. "The Department of Magical transportation had to fine a couple of people the other day for Apparating without a licence. It's not easy, Apparition, and when it's not done properly it can lead to nasty complications. This pair I'm talking about went and splinched themselves."
Harry had a sudden vision of a pair of legs and an eyeball lying abandoned on the pavement of Privet Drive.
"Were they OK?" he asked, startled.
"Oh yes," said Mr Weasley matter-of-factly. "But they got a heavy fine, and I don't think they'll be trying it again in a hurry. You don't mess around with Apparition."
-- HP and the Goblet of Fire
One thing we can say is that, if you Apparate without a license (a dangerous practise anyway, avoided even by many fully-qualified witches and wizards) you are quite likely to make a mess of it sooner or later. And when you do, you might find yourself in the lurch and require assistance from the Ministry of Magic ... who will fine you:
'You have to pass a test to Apparate?' Harry asked.
'Oh yes,' said Mr Weasley, tucking the tickets safely into the back pocket of his jeans. 'The Department of Magical Transportation had to fine a couple of people the other day for Apparating without a licence. It's not easy, Apparition, and when it's not done properly it can lead to nasty complications. This pair I'm talking about went and splinched themselves.'
'They left half of themselves behind,' said Mr Weasley, now spooning large amounts of treacle onto his porridge. 'So, of course, they were stuck. Couldn't move either way. Had to wait for the Accidental Magic Reversal Squad to sort them out. Meant a fair old bit of paperwork, I can tell you, what with the Muggles who spotted the body parts they'd left behind ...'
Harry Potter and the Goblet of Fire - p.63 - Bloomsbury - Chapter 6, The Portkey