Dealing with informative missingness
I don't see how embeddings can help. Embeddings serve to lower the dimensionality of your data. I think you just need to introduce a single feature that is 1 if there were people interested and 0 if there were none. Then if you have sufficient data, the convnet should be able to understand the relation between the time-series and the feature you added.

It's a bit hard without having any idea about what your data looks like, but you might also be able to ignore the missing data, and train a model that predicts a continuous time series. Then the model may flag an anomaly when there is data missing, but you only actually declare an anomaly if the data is not missing and the anomaly is real.