That may be the answer. However, it appears to be unduly complicated for my purposes, but it may be where I have to go to get the results I am looking for.

I can differentiate my parametric function before I plot it. The undifferentiated function is easier to plot than the differentiated form, so I was trying to avoid issues with numerically integrating the differentiated form.  ?NumericQ does not like my differentiated form and throws off garbage, whereas the undifferentiated curve plots smoothly.

It looks like ?NumericQ may need more work by Wolfram but it is a slick routine.