Personally, I don’t believe much would change. Throughout the Bellum Civile and the Bellum Africum Labienus is described as consistently vitriolic and staunchly opposed to Caesar and his soldiers. Now it could be Labienus felt betrayed by Caesar’s choice to to not submit to Pompeius and the Senate, but I believe it’s more likely Labienus felt betrayed because Caesar wouldn’t recognize his aspirations. Perhaps he may have dreamed of a consulship, eventually, or better recognition for his military exploits, things Caesar clearly denied him.
Thus, if Labienus does decide to stay loyal, Caesar would still go himself to Spain, and he’d still rely on relatively inexperienced officers like Gaius Scribonius Curio and Caius Antonius for the conquest of Africa and Illyricum respectively, to disastrous results. It wasn’t about their quality as lieutenants, but their worth in the overall political game. Caesar couldn’t afford to lose support of the young aristocrats of the 80’s who decided to coalesce around him, but he could very well afford to lose a political non entity like Labienus, who would certainly have had his part in the war, but probably not one more important than, say, Fufius Calenus, Caninius Rebilus or Calvisius Sabinus. So I believe Pompeius would still survive and reach Egypt, and things until 47 would go much in the same way. After all, Caesar didn’t stay that long in Egypt merely to hunt down Pompeius, who was already dead. It was part of a geopolitical strategy that entailed creating vassal kingdoms made of reliable people personally linked to him, like Kleopatra and Mithridates of Pergamum.
The African campaign of 46, however, would go more smoothly perhaps. Without Labienus employing his cavalry to wear down Caesar in a battle of attrition, while also avoiding a pitched battle, ironically the very same plan Pompeius had wanted to adopt for himself, Caesar could end Pompeian resistance much sooner.
The campaign in Spain of 45, on the other hand, would go much the same. The younger Pompeius was much more determined than Cato and Scipio to keep effective command of military operations IRL, so his strategy against Caesar, inadequate as it was, wouldn’t much change.
As for what concerns Caesar’s death, because no doubt Caesar would still be killed, Labienus could very well be a member of the conspiracy against him. A lot of staunch Caesarians like Trebonius, Decimus and Cimbrus defected, likely because they felt their careers were going to a dead end, without ever having their chance to be the man in charge, or the one to lead an expedition which would give them renown and fame. But if Labienus stays loyal, he wouldn’t become a political force of his own, no matter how much he was linked to Caesar, he was still a homo novus from Picenum, he could never aspire to play a prominent role in the oncoming war. He’d either side with Marcus Antonius or the Young Caesar, who would still rather rely on men personally attached to them like Ventidius Bassus, Gaius Sosius, Caninius Crassus, Agrippa, Statilius Taurus and Lucius Cornificius rather than an old man who belonged to another generation who had no personal connection to them and who’d likely have died of old age by the time Actium happened.
