Indeed. There are a total of three completely individual male lines in the US, along with an additional 3 separate lines in France, Japan, and Argentina. There are also a few other animals that have links to the current sires, however they are not direct offspring, and were sired by males that are no longer alive.
As for females, there are roughly 7-8 completely separate lines that are capable of reproducing. There are numerous other females I opted not to account for as they have type ins with the 7 or so "founding lines", so for sake of argument I left them out. There is one additional line, however I am hesitant to go over it, as the mother is completely unrepresented out side of her two offspring and is sadly deceased, however those two offspring were sired by the most over represented male in captivity, so I am hesitant to say it is a distinct line.
So to summarize, the captive population could sustain itself without any new blood and limited inbreeding for a relatively decent number of years, however eventually something will need to be done to add new blood.
Luckily, that problem is being solved as we speak. Russian Orca captures have taken place over the last two years, and even if they stop now, we have an additional 8 new wild caught founders added to the population. At least 3 are female and two are male, and there other 3 are unknown. At the moment 4 look to be heading to Russian dolphinariums, 2 look to be heading to China, and the fate of the other 2 are unknown, however there is rumour they might be headed to marineland Canada. That would be the best option, as their ageing female has no surviving offspring and less than 10 years of reproductive life left.
Additionally, Russian captures are likely to occur again, so our amount of new blood has potential to increase again. Although there is controversy over it (largely by the emotionally swayed "anti-cap" community), these captures are necessary to ensure the genetic health of captive populations, and like it or not these are animals are needed rather badly.
Oh, and to touch on Snowleopards post about cetaceans in Canada, everything you said is correct, however within the next 5-10 years, I would not be surprised to see those numbers increase at Vancouver. With the expansion of their currently facilities occurring, and through speaking to trainers at the aquarium, it sounds like they will be bringing in new animals once the expansions are complete. They currently have 2 animals on loan to Seaworld, and a third that he been down there for quite some time. I would not be surprised to see those animals and perhaps a few others return to the aquarium. As well, I would not be surprised to see more White Sided Dolphins, most likely sourced captive bred or rescued from Japan, or possibly even from the united states.
Marineland is also the largest powerhouse for captive breeding belugas on the planet, and they are not overly keen to share. Assuming they have animals of both genders they have also proven adept at producing orca as well. Sadly their last breeding male was thought to have a genetic anomaly, with many off his offspring having problems (seizures, stunted growth, compromised immune system, etc...) and the last of his line died out in 2009.
. Regardless, Georgia has the record for the largest single aquarium, the incredibly impressive Ocean Voyager.