Okay this is ridiculous. I mean come on. I guess I should say I am disappointed but not surprised...
Where do I even start? First of all there seems to be some confusion over what immersion means and how it works. Put simply, a game is immersive as long as you feel involved with the game. A game only loses its immersion factor for a player who begins to metagame; that is when his or her thought processes concerning the game stray to things beyond what the game has presented.
I know that immersion is often generically described as "feeling like you're in the game," and to be fair that is a good rough definition, however it can be a little misleading. It carries the connotation that immersion is linked with reality, the real world, and realism, but these ideas aren't actually present in a more accurate definition of immersion. Immersion is just the feeling of being involved with a game in terms of the game.
Confused? Wondering what this has to do with turn based combat? I'm getting there, just setting the foundation first. As I said, immersion is that feeling of involvement with the game as it is presented. Realism has nothing to do with immersion, and ascribing lifelike or realistic qualities to a game will not inherently make it more immersive. So what does make a game more immersive? What breaks immersion? The fact is, I can't answer those questions for anyone else any more than they can answer them for me. Immersion is highly subjective, it's a simple as that.
Now you may be wondering: "how can you claim all these things when so many people seem to agree that realism improves a game's immersion quality? Hasn't realism always been the direction games are headed?" Well, that's a tricky question. Some aspects of games have been trending toward realism, most notably graphics. However, that's not to say all games are becoming more realistic visually. Artistic stylism is a good example of this. But what I mean is as technology advances, potential for realism increases. And as potential for realism increases, so too do expectations for it. Again, that's not to say that all players want to seek out more lifelike games, but given the choice between two similar games, most players would choose the technologically superior one, all else being equal.
It should come as no surprise that different players have different gaming preferences. I hope that we can all be open minded enough to accept that. I myself am an avid final fantasy fan, and I would be hard pressed to find another series that certain people hate with such fervor. And it should be obvious that with different preferences come different technological expectations. Aside from a small subsection of people who specifically like retro style games and such, most gamers have certain expectations for technological improvements over time. The caveat here is that they expect those improvements in different areas depending on their preferences for the types of games that they enjoy. I guarantee you that nobody expects the next Final Fantasy to incorporate real-time motion sensory input, the next Street Fighter to feature advanced dynamic dialogue options, or the next Bejewled to run on a state of the art physics engine.
Let's recap, and then bring it all together. First, immersion is involvement with a game in terms of the game, it does not necessarily require an element of realism. Next, immersion is highly subjective. It depends on both the player's expectations and the game's delivery of them. Third, as technology improves, so do most player's expectations. Fourth, players have different gaming preferences, and no type of game can be held as objectively superior to another. And finally, a player's expectations depend on his or her preferences. If you're paying close attention you might notice how these five things are linked. Just in case you don't, I'll put it all together. A given player has unique preferences, which determine his or her priorities for raised expectations based on improvements in technology, and these heightened expectations translate directly to expectations for a game's presentation and delivery. This effectively sets a threshold, beyond which a game will exceed the individual player's expectations for a given prioritized feature. So long as a player's technical expectations are met or exceeded, he or she can no longer be subject to broken immersion. At that point, the player's enjoyment of the game is bounded only by the quality of the game itself, and not his or her perception of the game.
At last we can analyze the original question under the lens of this concept. Suppose for example a player plays a turn based game, say FFX. If that player is predisposed to enjoy (or at least not dislike) the turn based combat abstraction, the game will have met that particular technical expectation for this player, he or she will not consider it beyond what the game requires, and consequently there will be no detrimental impact on immersion attributable to the nature of the turn based system. On the other hand if the player is not inclined to enjoy (or especially outright dislikes) turn based combat, perhaps favoring the more realistic approach of real time combat, then the game will not have reached the player's technical expectations in that area. As a result, the player will be reminded of the shortcoming during every combat engagement, forcing them to consider the game as an entity beyond its own terms, thereby removing that element of involvement with the game, and negatively affecting the player's immersion.
So you see, broken immersion does not follow directly from lack of realism unless the player finds it undesirable. The same holds true not only for realism, but for any aspect of any mechanical feature of a game.
tl;dr
As long as a player finds turn based combat in a particular game acceptable, it cannot break that player's immersion. This is ENTIRELY subjective.