Not exactly. Suppose that L is the length of the strings you are trying to match. With the naive approach the RE engine can take advantage of Boyer-Moore, so its running time should be about O(N * M / L). With the trie approach the number of times that the re engine will start trying to match is O(N), however each attempted match that fails can cost up to O(L), so your running time is potentially as high as O(N * L). (Usually you won't hit this worst case though.)

If you have a lot of strings to match, this is potentially a big win. If you have a small number of long strings to match, this is probably not a good optimization.