If they were armed with ML-16-grade lasers, it would be absolutely possible.
That is nothing more than a supposition, but again nothing says that Shivans capital ships have shields. How do you expect the Ancients to take down the Shivans capital ships when they have a proper fighter cover with nearly-indestructible shields, and bombers with again nearly indestructible shields ? How long would we have hold weren't it for the Avenger cannon ?
We would fly a Dragon that was discovered in Roswell to the Lucifer fighter bay, hack the Shivan shield system with an amateur trojan and then launch a Harbringer straight into their flight control, showing the Shivan flight controller our middle finger before escaping the shockwave...
Wait, I think I've seen this already somewhere
Aside from that, I always wondered how advanced the Ancients were. It was said by Volition that they were only just a little bit better than the Terrans or Vasudans... but from which period ? FS1 or FS2 ? If FS1, then I can easily see how they could get raeped by the Shivans. I mean, look at the Terrans and Ancients. What's the biggest difference > We encountered an enemy that was a hard nut to crack, but weren't indestructible - the Vasudans. We were at war for 14 years, developing new technologies and weaponry all the time, so that when the Shivans came, it didn't take us long to adapt. In a matter of months, we have improved our scanners, and laser weaponry like Banshee or Prometheus evolved from "fancy toys" to basic weaponry. We managed to utilize land weaponry for space usage (the Harbringer).
WARNING: PURE SPECULATION AHEAD !
On the other hand, the Ancient could have never met anybody like that. They ventured deep into space, subjugating everybody. After all this talk about how the Destroyers are actually the Preservers, who eliminate highly advanced races so that the lesser ones can have a chance of development, it's quite possibly that most of the enemies that the Ancients encountered were probably even barely capable of space flight. They didn't have to bother with upgrades, because if there were any problems it was them who had the numbers. They just flooded enemy system and took it over.
And then they encountered the Shivans. A single system of them. But they didn't want to die. It could be understood in many ways. Perhaps it's about their numbers; as observed during FS1 and FS2, for every Shivan fighter we kill, a new wing of them appears
Or maybe it's the shields - remember the first mission with Shivans ? You could hit a Scorpion with the ML-16 for literally ages and it would not die... The only way of killing it was to use Furies to take down its shields.
And then the Shivans got pissed and started killing Ancients. System by system, cluster by cluster, galaxy by galaxy. They had te number and the time to do this. And the Ancient, not being used to adapting, couldn't help but watch as they get owned.