As far as we know yes, he really was.

The episode is mentioned in two ancient biographies of Caesar - Plutarch and Suetonius. I don't know if 'fan fiction' is quite the right term, but the account has probably been embellished a bit. Certainly the parts in Plutarch where he dazzles the pirates with charming speeches about how he's going to murder them all seem a bit far-fetched. Nevertheless, there's no real reason to doubt the basic story that he was kidnapped by pirates as a young man. Piracy was a serious problem in the Eastern Mediterranean at the beginning of the first century BC, until 67 when Pompey was granted a huge extraordinary command to deal with them.

Yes, at least according to ancient sources. Here is Seutonius on it in Lives of the Twelve Caesars:

While crossing to Rhodes, after the winter season had already begun, he was taken by pirates near the island of Pharmacussa and remained in their custody for nearly forty days in a state of intense vexation, attended only by a single physician and two body-servants; for he had sent off his travelling companions and the rest of his attendants at the outset, to raise money for his ransom. Once he was set on shore on payment of fifty talents, he did not delay then and there to launch a fleet and pursue the departing pirates, and the moment they were in his power to inflict on them the punishment which he had often threatened when joking with them.

Plutarch also writes about this incident in his Parallel Lives:

on his voyage back, was captured, near the island Pharmacusa, by pirates, who already at that time controlled the sea with large armaments and countless small vessels.

To begin with, then, when the pirates demanded twenty talents for his ransom, he laughed at them for not knowing who their captive was, and of his own accord agreed to give them fifty. In the next place, after he had sent various followers to various cities to procure the money and was left with one friend and two attendants among Cilicians, most murderous of men, he held them in such disdain that whenever he lay down to sleep he would send and order them to stop talking. For eight and thirty days, as if the men were not his watchers, but his royal body-guard, he shared in their sports and exercises with great unconcern. He also wrote poems and sundry speeches which he read aloud to them, and those who did not admire these he would call to their faces illiterate Barbarians, and often laughingly threatened to hang them all. The pirates were delighted at this, and attributed his boldness of speech to a certain simplicity and boyish mirth. But after his ransom had come from Miletus and he had paid it and was set free, he immediately manned vessels and put to sea from the harbour of Miletus against the robbers. He caught them, too, still lying at anchor off the island, and got most of them into his power. Their money he made his booty, but the men themselves he lodged in the prison at Pergamum, and then went in person to Junius, the governor of Asia, on the ground that it belonged to him, as praetor of the province, to punish the captives. But since the praetor cast longing eyes on their money, which was no small sum, and kept saying that he would consider the case of the captives at his leisure, Caesar left him to his own devices, went to Pergamum, took the robbers out of prison, and crucified them all, just as he had often warned them on the island that he would do, when they thought he was joking.

Though it should be noted Plutarch was more concerned with the character of the subject, rather than historical events, so some of this version story may have been exaggerated to highlight Caesar's awesomeness. Though I think it's safe to say that he was held ransom by pirates that he later hunted down.