As long as it is either:
a) a single player game,
b) a multiplayer game where it is the host doing the changes before processing the turn, then sending out the altered data files,
most changes to the data files or AI files (well all to the AI files) will be reflected in-game immediately for a SP game or the next turn for a MP game. As Douglas said, do not insert new items in the middle, or you will break your savegames. Insert new items (even new levels of a component, such as a Space Yard IV) at the end of the file. You can safely move them to a better location before you start your next game, just not for the current game. Also, be very careful about changing sizes of components. You might get invalid designs, which you will never be able to build, or remove from the designs list. Same goes for removing a component by setting is tech reqs to 100 or so (maybe to remove that Version and add a new, altered Version).
Note that changing some files has no affect on a savegame, as many files are only read either when you create your empire file or when the game is started. Reference the end of the
Getting Started chapter of the SEIV Modding 101 Tutorial for a chart which explicitly lists all files and their ability to affect savegames. The rest of the Tutorial is a good place to get modding help.