It's highly unlikely to say the least, though technically possible. Roman politics were full of accusations and slander like this (Cicero, who abused Clodius and later Antony--at the cost of his head--mercilessly, was the master) and we needn't take every word literally. The first reason we have to believe that Antony was just trying to weasel his way into the head of the Caesarians, which by Caesar's will Octavian would've inherited, bearing the magical name of Caesar, to which the Caesarian veterans were loyal, was that such accusations are not raised until Octavian appears in Rome. Upon Caesar's death, Appian tells us, Antony raised no objections when the will was read aloud and gave a funeral oration for Caesar that made no mention of the will--in fact, Appian says that the only problem with the will was that people were angered that Brutus was mentioned as the secondary candidate of adoption (Roman wills usually specified a second candidate for adoption in case the first died or refused). Now, Appian is wrong, because Caesar's will was not read until the 19, a full day before Caesar's funeral, but the point remains.

The second, and vastly more important, is that Antony's political position was put in serious jeopardy by the presence of Octavian in such important political power. Far from being Caesar's right-hand man, as Antony liked to boast of himself, Mark Antony, by the time of Caesar's death had been largely cast aside. While Antony had served Caesar as an able military commander (and even in this regard he was considered a substitute for Labienus, who had defected to Pompey and was far and away Caesar's best military subordinate) his complete failure to administrate Italy while Caesar was out fighting the civil war forced Caesar to publicly scold him and strip him of all public rank. Although Antony appears to have remained loyal to Caesar, Caesar never once trusted Antony again. Many scholars (including myself) highly suspect that Antony may have had a part in Caesar's death. Antony had the most to gain of an man in Rome from Caesar's death. We know that Antony had been approached in an earlier conspiracy and had refused, exposing the conspiracy and ingratiating himself with Caesar. This resulting in slightly more trust in Antony, and his appointment as Caesar's colleague during his consulship in 44, whereas his consulship of 45 had had no colleague (it was intended for Antony but Antony had fucked up). Caesar's death rather conveniently coincides with his partial return to Caesar's favor. I say partial because it was hardly complete--Caesar treated Antony as a yes-man and a lap dog, keeping him far from the important affairs of the state, since he feared that Antony would fuck up again. But it was enough that in the event that Caesar was removed there was no one high up enough among the Caesarians to challenge Antony, who could (and did) also point to his past services to Caesar to back up his authority. Whether or not Antony was involved in the conspiracy (and he certainly knew about it, that much is pretty sure) Antony definitely benefited the most from Caesar's death. All of a sudden he became sole consul, and as the only major Caesarian left who had commanded the army he now had the loyalty of the largest body of the most experienced troops in the history of the Roman state. Since Caesar had effectively removed the vast majority of his political enemies from the inner workings of the state, his successor had total control over the state. This was made official when Calpurnia, Caesar's widow, produced papers stating that Antony was, by will of Caesar, to be named his legal heir and commander of the Caesarian troops. Antony didn't realize that he didn't actually have anything but an empty bag until the 19, when Caesar's will (which had been rewritten when Caesar returned to Rome in 45) was read and Antony realized his mistake. Oops. Well, it didn't really matter did it? After all, Antony had already by this time taken steps to eliminate the tyrannicides from Rome and was in sole command of the army. And this Octavius guy was some upstart nobody had ever heard of who barely knew Caesar (Suetonius says that Octavius met Caesar once when he came ashore after the ship that was to bring him to Spain to serve under Caesar was wrecked and he walked through enemy territory to Caesar's camp) and who was totally inexperienced in the complexities of Roman politics. As such, Antony continued to act like Caesar's heir, passing laws and making decrees in Caesar's name, such as the Lex Antonia which abolished the dictatorship and essentially ensured that the leader of the Caesarian party (himself) would gain the support of the senate by not holding official power. Unfortunately Antony miscalculated and ended up alienating both the Republicans and the Caesarians, because in trying to play both sides he had only pissed them off (yep, he bungled politics. Again). Octavian turned out to be a much more able political opponent than Antony had expected, borrowing vast sums of money to donate to the citizens of Rome (since Antony had refused to relinquish Caesar's fortune, which Caesar's will had stipulated was to be spread out to each citizen of the city), which netted him a large number of political acquaintances and the support of most of the Caesarians. Octavian then proceeded to side with Cicero, who regarded Antony as a menace, and encouraged him to deliver the Philippics, a series of invective speeches against Antony widely regarded as Cicero's harshest (no but seriously the things he says in there make the things he said to Clodius, like that he was sleeping with his sister and was a disgusting pervert, or to Piso, whom he accused of being a Syrian slave, look like praise). By November Octavian's position was already so secure that he could start stealing legions from under Antony's nose, despite the fact that he legally could not command them (not that Octavian gave a shit, and he essentially commanded them as a gigantic personal bodyguard). It was during this period that Antony began lashing out against Octavian, who had refused to play nice and do as he was told, accusing him of forging Caesar's will and so forth. Even Suetonius, who relates these accusations, says that this was pure slander. And it was rather inept slander as well, because unlike Cicero, whose wit could let him get away with nearly anything, Antony was crass and uncultured, and rapidly put his foot in his mouth, simply pissing even more people off. But Antony was determined at this point to do anything that it took to fight off Octavian, and when this failed he made the somewhat foolish move of marching north with his army to seize Cisalpine Gaul (which he wanted as his proconsular province instead of his assigned province of Macedonia), which gave Octavian the perfect excuse to ask the senate for extraordinary powers to take his personal army north and stop him, which they immediately accepted.

So on the balance it's not likely. It's not recorded by most of our texts, and those accusations just sort of pop up out of nowhere, in the middle of a rather panicked string of political attacks that Antony made at the time in order to try to keep his stranglehold on the Caesarians without having to admit that he was neither an adept political leader nor a legitimate heir to Caesar's fortune and armies