"other" class in Image classification
You can have that but I recommend something else for your case. Suppose that you have 10 classes of digits that they are mutually exclusive. Consequently, your output vector will always be on-hot encoded. In a simple case, your output vector should contain ten entries for each class. To make your model distinguish between those inputs which are digits and those which are not, do the following:

Increase the size of output to eleven. Provide data-set that contains eleven-entries labels. the first entry corresponds to the existence of a digit. If it is a digit the first entry should be one and next 10 entries should be activated for the according to the value of the digit. So, your labels will not be one-hot encoded. If the input is not a digit the first entry of the output should be zero and other entries are don't cares.