There isn't enough solder in the holes to run down the board. Surface tension will hold it in the hole until you draw it out with the pump. When desoldering the holes be careful not to leave the iron on the point for too long. You have a low wattage iron which is good for small component work, but it is still possible to burn out bits if you keep the heat on for too long. Also, avoid trying to drive the tip though the LPC hole when desoldering. It's ok if it does push through while you are working but you don't want to force it. Too much pressure may squeeze the LPC hole ring onto the iron tip and then it could pull off on removal.
Does the stand that came with your iron have a sponge pad? Some do, and this is a great item to have. When you are getting ready to work with the iron be sure to give it time to warm up. If you try working with the iron before it reaches optimal temperature things will just be difficult. Once heated you'll want to put a little bit of solder on the tip of the iron to help the heat conduct. You really don't need much, and if the tip is good it should flow onto it rather than create a ball that looks like it could roll off. The tip of the iron should be cleaned every now and then, this is where the sponge I mentioned comes in. You want the sponge to be damp, but not so wet that it would leave water in your hand if you rested it there for a moment. When putting the iron back in the stand brush the tip on the sponge. You should have a nice silver shine on the tip when you put the iron aside. This cleaning will help keep the iron in a condition where it will properly hold solder and conduct heat. If you start getting black crud on the tip you may need to replace it. I've got a real nice iron that has lasted me for 15 years now on the same tip. Proper care and cleaning when being used has kept it this way. (This isn't the iron I use to mod Xboxes. This is a variable temp high wattage unit with a big screwdriver tip that I had initially purchased it to assemble RC car battery packs. Imagine trying to solder something that looks like desoldering braid to the ends of a C cell battery. You need a lot of heat and you need it to transfer quickly.)
A flux pen will only help solder to flow between components. For desoldering (especially if you're using a pump) I don't know if there will be any benefit to applying flux.
FYI, all 1.0 Xbox units had the LPC holes filled in. I had done the same procedure Martin recommended to clear my LPC out. Board supported on end, iron on one side pump on the other. Worked pretty well. I had to do this because I was hell bent on installing via pin header. (While the wire install would have been easier I'm still happy with the header.) With the solderless adapters you really shouldn't need to clean out the holes. With or without solder they should work. The problem that the solder throws into the mix is that it doesn't let the pins drop down into the holes and make contact with the board traces themselves. The pins bottom out on the solder which tends to oxidize more quickly than a bare point on the board would. A good cleaning as Martin had recommended earlier, or alternately I've seen a pencil eraser suggested, will usually clean this up.
-Whoopin
