Hardly. They would have enough ships left to salvage working parts and somehow make it away from there. Especially considering Gargantia's gunners seemed poor in comparison to the pirates. In any case this was a special situation since the pirates were out for blood after Ledo's earlier stunt. I guess Gargantia could have now wiped out this entire clan of pirates, but if we assume pirates work together (in order to manufacture stuff), then there's no knowing if the rest of the pirate clans would try to retaliate. It was explained quite explicitly in this episode that the balance of a sort that exists needs to have the pirates to stand higher on the dangerousness scale. If Gargantia's crew was made of cutthroats, they wouldn't care and would have, now that they have Ledo, started a campaign to kill everybody they don't like, pirates and competitors included, but fortunately they aren't such killers. They are civilians wanting a peaceful life for themselves and their children.
Not that they could even count on having Ledo and Chamber for any specific amount of time. They could have slaughtered all the lobster pirates now, but what if Ledo had disappeared a week later? They would have needed to face the rest of the pirates with few means of defending themselves. Other civilian ships and fleets might have also started to avoid them, in fear of being linked to Gargantia in pirates' minds.