With machine learning algorithms it is often beneficial to use feature scaling or normalisation to help the algorithm converge quickly during the training and to avoid one set of features dominating another. Take, for example, the problem of predicting stock prices. If you include high priced stocks such as Apple or Microsoft along with some penny stocks, the high valued features you will necessarily extract from Apple and Microsoft prices will overwhelm those that you extract from the penny stocks, and you won't be training on an apple to apple basis ( no pun intended! ), and the resultant trained model might not generalise very well.
However, imho "attempting to decycle and detrend the data" would be a very good thing to do. Extracting the various cyclic and trend components and normalising them by subtracting their respective means and dividing by their standard deviations would place all the data for all time series into the same approximate range, and then you would be training on like to like data which, when rescaled by reversing the normalisation, would likely generalise much better for predictive purposes.
Furthermore, for any time series it might be the case that trend swamps the cyclic component, so you might end up training on trend only data which almost certainly won't perform well on cyclic time series, and vice versa. By separating out the two components and training on each with separate SVMs or NNs and then recombining the two predictions, you might end up with a more accurate and more readily generalisable algorithm.