I've been putting off having a technician come out to deal with the pipe angle issue, although like you say, it may not be as difficult to correct this problem as I'm anticipating.
No. Ours are split-system wall units. I'm not sure if this is what you refer to as central units in the US. In Australia, what we refer to as split-systems look like these: Please Register or Log in to view the hidden image! The pan is in the unit like the one above. It is angled to drain to a pipe outside. The unit outside looks like this: Please Register or Log in to view the hidden image! My parents house had one and it was not angled properly for the one in their dining room and would have water coming out of the system and dripping off the system and down the wall. When they had it fixed, it was discovered that it was because the pan was not angled properly to drain into the pipe that would take that condensation outside. I know with ours, and we have quite a few of them (we had central ducted a/c, but elected to remove it and replace it with split-systems as they are actually cheaper to run for us as we turn it on when we are in the room when we need it, instead of zoned which would often see unused parts of the house in that moment also being cooled), we do not get any type of sludge that Wegs mentioned. It could be because it is angled to drain properly, so the water isn't remaining there stagnant and growing bacteria. As a precaution, we always have it serviced and cleaned yearly, to disinfect the pan and drains. Because otherwise, they can get a bit smelly, even when it is configured properly and if it is being used a lot in very hot and humid conditions.