Does testing a training dataset guarantee successful results?
This is correct, there's no guarantee at all, not even a high probability. As usual It depends on the type of model, the data, the number and distribution of the classes.
However there's of course a higher chance that the instance would be correctly classified. That's why one shouldn't use a test set containing training instances to estimate the performance of the model, since there's a high risk the performance would be overestimated (data leakage).