Is it common to add noise to Time Series data before training a model
I'll go through your questions one by one:


  I once read about somebody who added noise to their time series before training a model. They didn't write why they did it though.


No, noise is not adding any value to your dataset. The reason is that noise, by definition, cannot be learned by any statistical/ML model.




  Is this common practice?


No it's not.




  why do people do it ie. to prevent over-fitting?


It's not a technique that helps you in preventing overfitting. There are several techniques to do it (ensemble modeling, cross validation), many of them depend on the kind of model you want to implement (such as recurrent dropout for RNNs).