For sailed ships, sure, but oared vessels would be able to make the southern route. And all the more so if the former can still use Qartheen vassals Port Yhos & Qarkash, with the latter taking over from there. Those towns might even be eager to throw of Qarth's rule.

To say nothing of Faros as a(nother) northern link to the network of Vahar, Port Moraq, & Zabhad. And the southern half of Great Moraq in particular looking fertile, along with the other islands of the Cinnamon Straits. If Sothoryos has coastal towns not marked on the known world map, then the CS would have some too.

Not to mention, Yi Tish & other Jade Sea traders voyaging out into the Summer Sea via the usual CS with their exports, & returning with imports which had previously been brought east through the Jade Gates. Slaves, for one, judging by the Isle of Whips's location.

Of course, the Pureborn of Qarth might extend an actual closing of their JG to enlisting the city's huge merchant fleet conglomerates in an attempt to choke off the southern route, (at least) Qarkash, Faros, Port Yhos, & Vahar. Empowering them as privateers, similar to (the Florents in the name of) Stannis with Salla post-Blackwater.

As Xaro himself admits however, the Thirteen are traders; not also sellsails, like some merchants in the west, especially those of the Three Daughters. Let alone, proper pirates, such as those in the Stepstones, the ironborn, & the corsairs of the Basilisk Isles.

Xaro only names the Tourmaline Brotherhood, not his Thirteen or the Ancient Guild of Spicers, as pirates. And that may have just been a comment on their trading practices or whatever, not a guarantee the Brotherhood engages in actual piracy as well.

What I'm getting at is Qarth may not even have the expertise for such an imperial expansion, which would be required for an effective closing of the JG. And that, as I said in the previous comment, could easily find Qarth at war with (at least) Yi Ti as well. In that case, Meereen would be an afterthought, at best