Turks are classified as a pest species in a few states. I think Arizona, southern California, New Mexico and Texas.
Some things to note. As Barbara mentioned, they just don't escape nor are they really inclined to try and escape. Aside from user error (ie: you knock the bin over on its side) they really aren't going to get loose. Turks are much like wood roaches and they prefer being outdoors (probably because of the humidity) and will usually head back outside if they should get loose. They are also very dependent on humidity and temps to breed and grow. Only a few places in a home could provide both of those (compressor and drain pans on the fridge, a leaky bathroom sink) and that means they are limited to where and how they breed. Infestation, no probably not. Can they survive and possibly have babies once or twice, possible. In reality, conditions are not right in the home for them to do this, much less truely infest.
The room I keep my Turks in ranges from 82-92 degrees during the summer months. During this time of the year it is 68-82 degrees with the average around 78 or so. I have noticed a HUGE drop in production during these colder months now and see very few females carrying an ooth and a lot less hatchling nymphs. Below a certain temp, they just seem to cut off the breeding. I think in an average home they may do ok during the summer, but come winter they would be wiped out.
I live in an old home and always have a problem with American Cockroaches coming from the outdoors during this time of the year. I can't stand them and am very skeptical of Turks because of this. With all that being said I keep em and have no problems doing that. I think they could infest given the right conditions, but even my old beat down home wouldn't suffice for them. Lack of food and moisture coupled with the lower average temps, they wouldn't survive through the winter.