Mecha-Frieza experienced a different fate in Future Trunks’ timeline in Dragon Ball Z. In the anime, he was famously killed by Future Trunks upon his arrival in the present. For this reason, it’s impossible for him to have met the same end in the other timeline.
The Z-Warriors were placed in great peril when Frieza came to Earth in pursuit of revenge against Goku. Joined by King Cold, Frieza was about to attack Goku’s friends when they were saved by the timely arrival of Future Trunks, who managed to kill both Frieza and his father. Thanks to him, neither villain succeeded in bringing any harm to the Z-Warriors. Interestingly, the way in which Dragon Ball Z killed off Frieza raises questions about what happened to the character in Future Trunks’ timeline. Since he wasn’t even born yet, he obviously couldn’t have been there for the fight with Frieza and King Cold.
Since Piccolo, Vegeta, Krillin, and all the others lived long enough to be killed by Android 17 and Android 18 in Future Trunks’ timeline, it stands to reason that Mecha-Frieza was defeated in its version of these events as well. How that happened was hinted at during Goku’s first conversation with Future Trunks when he explained his Instant Transmission power. Trunks explained that Goku was supposed to beat him, but when Goku didn’t arrive, he stepped in and handled both villains. This prompted Goku to explain that he was planning on fighting Frieza by using Instant Transmission to get to Earth right away. However, it seems he sensed Frieza’s defeat and didn’t need to take any action. Since Trunks wasn’t around in the other timeline, that means Goku’s intervention was necessary.
In other words, Mecha-Frieza and King Cold would have been defeated regardless of what Trunks did at the beginning of his Dragon Ball Z arc. Their defeats simply happened at the hands of a different Super Saiyan. Since Goku’s fight with Future Trunks proved that the former was still the stronger fighter, there’s no doubt that even with King Cold around, Goku would have had as little difficulty as Trunks did in beating them. Frieza and his father dying as a result of their battle was implied, but not explicitly confirmed. Since Dragon Ball Z’s Goku had a no-killing rule, it’s unclear if he destroyed them unintentionally, Vegeta finished them off, or Goku just drove them off the planet.
Though Goku’s fight with Frieza is considered to be one of the most challenging battles he’s ever endured, a rematch in the Android Saga would have been extraordinarily lopsided. And while a confrontation would have been interesting to see, it wouldn’t have been able to compare with what Dragon Ball Z delivered. Even if it didn’t need to happen, Future Trunks cutting Frieza in half and blowing him to pieces is still considered one of the most shocking moments. Not only that, but it amounted to a thrilling introduction for a now-iconic character.