Yes, you can. BigML can handle missing values automatically for categorical, text, and items fields. For categorical fields missing values are handled as another category. However, in text and items fields (where contents are handled as sets of terms or items), missing values are treated as an empty set.
On the other hand, BigML does not support missing numeric values. Instances with missing numeric values will be ignored by default, but you may optionally choose to replace those missing values with a non-missing value (such as the field's minimum, maximum, mean, median or zero). You will want to do this correctly, since the wrong choice for an imputation value can lead to poor clusterings. Click here to see how to treat missing numeric values to build clusters and centroids.