The range of the Illuminator is less than the range of the Guardians Repulsion (the Illuminator has the least range of all the LRF's, after all). As a practical matter though, Illuminators can sit just sit near the Guardians and be firing off their beams because many ships will be able to get a bit into a Repulsion field (they just have difficulty really getting in close to the Guardians usually). The Illuminators will usually not be able to use their greatest advantage, bringing all three weapons to bear, but if you're just trying to hold off a superior fleet, that isn't too much of an issue.
If you're keeping a fleet using Guardians, it's often to keep your units on Hold Position to avoid the problem Raging Amish mentioned of units chasing enemies out of the Repulsion field and off into the jaws of your enemies. This ensures none of your units stray to far or your Guardians wander off, and usually a good way to fight defensively as Advent.
But anyway, against the AI in general, Repulsion with Malice and Cleansing Brilliance can be a very potent combination. You can use your Malice and Cleansing Brilliance, then simply push away the enemy fleet while you recharge (a Radiance using Guidance can help hasten the Cleansing Brillinace recharge cool down if needed). Then once charged you can let them in close and give them another hit. Fighting from a world with multiple Repair Bays to cover damaged units, and if possible an Antimatter Recharger or two will help you in longer battles. If the AI has taken a liking to Carriers/Transporters/Drone Hosts, going heavy flak or getting a couple Halcyon's with Telekinetic Push should help solve the problem.
This works best against Advent AI's since even their Illuminators will have difficulty hitting you and the Destras are more or less out of the picture. Against a Vasari AI it can work fairly well, although the longer range of the Assailant can be a problem, but the biggest issue is the Subverter, it has to get fairly close to use Distortion Field but quite literally all it takes is one getting through and hitting your tightly packed fleet and you can lose your Guardian's Repulsion and Shield Projection, then you're in trouble. Against a TEC it depends on the number of Javelis there are (they significantly outrange Repulsion, can easily strike at things inside the field, or the Guardians themselves), a large number of Javelis can simply shred the fleet safely.
This generally doesn't work against a person either, since there are a variety of counters to the tactic once they see it. They will often go heavy LRMs to get you outside your Repulsion range, use a number of Strikecraft, various Antimatter stealing/disabling abilities, or they may just bypass you altogether since it will be much easier to glass planets than deal with your annoying fleet that is just trying to keep them busy.
But the AI will grind itself to dust on you.