Trying to include all of the spiderwort-type Tradescantias into one behavioral description is a mistake. Among the various species, cultivars have been developed, some of which are sterile. Location would also be a huge factor in how any particular one behaves.
Look at how many plants, from several species of Tradescantia to various cultivars thereof, and even a few plants from other genera share this nickname:
http://garden.org/plants/searc...
Such small, herbaceous plants are not difficult to evict from a garden, just dig up all of the roots. They can be bigger than expected, and always impossible to pull unless your soil is *really* soft down to about a foot deep: