You have to try it: the answer may vary based on your corpus and application-specific perception of 'similarity'. Effectiveness may especially vary based on typical document lengths, so if "rapidly growing with time" also means "growing arbitrarily long", that could greatly affect what works over time (requiring adaptations for longer docs).
Also note that 'Paragraph Vectors' – where a vector is co-trained like a word vector to represent a range-of-text – may outperform a simple average-of-word-vectors, as an input to similarity/classification tasks. (Many references to 'Doc2Vec' specifically mean 'Paragraph Vectors', though the term 'Doc2Vec' is sometimes also used for any other way of turning a document into a single vector, like a simple average of word-vectors.)
You may also want to look at "Word Mover's Distance" (WMD), a measure of similarity between two texts that uses word-vectors, though not via any simple average. (However, it can be expensive to calculate, especially for longer documents.) For classification, there's a recent refinement called "Supervised Word Mover's Distance" which reweights/transforms word vectors to make them more sensitive to known categories. With enough evaluation/tuning data about which of your documents should be closer than others, an analogous technique could probably be applied to generic similarity tasks.