It sounds like a fun thing to try! Barbs seem to gravitate and home in to undefended cities so it probably would not take long to lose it to them.
I routinely hunt and bribe and kill all the barbs I can, esp. land barbs (sea barbs I sometimes just kill on sight). By coincidence, in GOTM 16, the barbs had captured an AI city on a continent, so I kept a dip near it and bribed all the horsemen coming out. Their production rate seemed slow, probably because of small city size and undedeloped terrain. Anyway, it did supply a nice trickle of non-vet dragoons and cavalry as Leonardos upgraded my newly bribed barbs.
Once I hit Magnetism, all my carrying ships have at least one dip. When Barbs land to attack the AI, if a ship is in range, I rush over and bribe all the attacking barbs I can, and hopefuly kill the leader, which easily pays for the bribes.
In some undeveloped places, it seems the barbs come pretty often... if I find one of those spots (near the AI), I'll set up shop and collect lots and lots. I think that happened in GOTM 6 or so last summer (the one where the human was German, and began on the same continent the Zulus on a relatively small map).
So especially for Democracy/Republic, barb trolling can be both fun (like a "puzzle" within a game), and useful. Make lots of dips and spread out... you'll find them!
PS, Having a barracks might not guarantee vets, as improvements (either Group 1 or Group 2) are lost when the barb takes your city. In a small city, with only Barracks, there is a disposition to allow the barracks' Group to "win the toss" .... Other improvements in the Barracks' group (the "defensive group") include Library, City Walls, Bank, University, Colosseum, Stock Exchange, Coastal Fortress, Harbor, and a few more late game improvements.
At any rate, the barracks might not be that significant, since presumably the human will build Leonardos, which will upgrade the units by the time you pick them up and transport them somewhere
.
If you're going to have one such city, why not try a "dense pack" of a bunch of cities (without barracks) and keep the supply coming steadily?
. They'd be ripe for trolling every time the troll ship could make the round trip!