Yes, with practice, you could learn to control every toe individually.
The reason it is difficult, is that the part of your brain which is responsible for voluntary movements, the motor cortex, has relatively little area devoted to your toes. Here is a representation of the relative area each body part has in the motor cortex:
The more area devoted to the body part, the better voluntary control you have over it.
The motor cortex also shows a high degree of plasticity. That is, practice induces measurable changes in the brain: the area devoted to the specific body part increases, and control over a body part improves as a result.
Amputees are a living proof of this. Some of them have developed the ability to carry out everyday tasks using their toes, even writing.
However, should you spend time learning such skills? Most likely, not. Also, "getting aware of every muscle and learn to control them" is too generic to have any meaning.
For example, the toes are extremely useful in balancing. (Try balancing on one leg with an injured big toe!) If you practice a lot of yoga poses balancing on one leg, your toes will develop the necessary skills to work together with the rest of your body to achieve balance. You, then, might become conscious of your toes working skillfully.
This is probably what your teacher meant when she said it took her some time to control her pinky toe. She did not spend her time trying to "control every body part" separately. She has practiced specific skills, that were relevant and useful to her. For example, balancing, which involves the whole body, with the parts working together in harmony. Then, she became aware, that the parts, eg. the toes, have improved in their skill.