The configuration of the gear can in fact be a mix of up to three possibilities between the various components: fully balanced, balanced I/O but not internally, or single-ended where the XLR jacks utilize only the hot portion of the signal. Either of the first two configurations might be worth experimenting with balanced connection, though even in the first case and especially in the second, results might not be clear-cut in favor of balanced. There are really four auditioning outcomes possible if it's a controlled test (meaning done with the same kind of cable both RCA and XLR, and at matched volumes):
1) You hear no difference.
2) You maybe hear a slight difference that you're not sure is an improvement, but anyway is too slight and elusive to make switching worth the trouble and expense.
3) It makes the sound worse (yes, it's a real possibility in some situations).
4) It makes the sound definitely better and is deemed worth the trouble and expense of switching.
Even in the case of gear that only provides XLR jacks which are effectively single-ended, there could still be a difference in the sound due to nothing more exotic than the fact that a different type of jack is being used.
So I beg to differ with the absolutists going either way. A lot of this question also depends on the hearing accuity of the listener, the resolution of their system, what they define as being a worthwhile improvement, what their system and listening priorities are, what the budget is, and what kind of cables they're using now. And all bets are off if the balanced cables they're considering are of a different kind than the RCA ones they're presently using. All of the preceding is in addition to the question of what the configurations of the partnering gear's I/O capabilities may be, which in itself also contains both the theoretical and the actual aspects of performance, which in turn are also affected by the environment the gear is used in. And then there's the question of possible differences in the handling of the ground connections, which could have effects on the noise floor...In other words, there are just too many variables to start laying down absolute laws about outcomes regarding this whole issue.
So as I said before, the only sure-fire way to know what's up for you in your system is to try it out and listen. Hammerfilms (great username, BTW!), since you already have some balanced IC's on hand, what you need to do is simply run the experiment yourself using just the stereo mains and leaving the other channels disconnected (to eliminate potential additional ground-plane noise). Obviously, the most diagnostic test would be to use the same kind of cables for both RCA and XLR, and try your best to compensate for any level diffences using the volume control prior to serious auditioning. Time go beyond asking the forum to stand in for your own ears! :-) Let us know your results when you do...