Its actually a complex subject. But, essentially, yes.
If I am providing too much info I apologize in advance...
In a nutshell, the reason why people sparge is to increase their efficiency - to get more sugar out of the same amount of grain. The initial reason for doing this was money. Same amount of grain but more wort.
For the homebrewer I suppose some of it is still money. But its also a volume issue. You only have room for so much grain. So you try to get more wort from the maximum grain your system can handle.
But with sparging, there are trade-offs. Eventually you start to get more than just sugar in the run-off water from sparging - and can end up with an increasing astringent taste from what I understand.
I batch sparge and according to research I read here in the wiki section, 2 batch sparges seems to be a good compromise between efficiency and oversparging so that is what I do. My volume for each sparge is close to my obtained volume after mashing. This seems to work well.
With fly sparging and collecting wort through run-off, it's my understanding that people will collect run-off until a certain gravity is reached. Some will stop it short when a certain volume is reached. But if you stop short early on, you will lose some converted sugar still left in the grain and your efficiency and therefore OG will be effected.
If you get too much wort, yes you have have to boil down to your target initial boil volume and then start your true boil and hop additions from there.
Sorry to be long winded.
Hopefully someone who fly sparges will chime in at some point.