I think that you want to "eat your cake and have it, too." Either the value is unknown (missing) or it is known (not missing). Using a value label was meant as a short cut in the data column. The JMP platforms, such as Graph Builder, generally work with the values, not the labels. An observation will not (should not) be included in a linear regression, for example, if its response or predictor value is missing, regardless of any assigned label.
You might re-think your approach and see if the label is actually necessary in the first place. Does it make sense to plot something that is unknown? (I can understand if you want to analyze the number of missing values but not individual observations.)