NO! Please do not remove the cartridges! If you do, the heads will dry out and you will be in much worse problem. Never remove or let the carriage sit in the middle of the printer. Always let it come to rest of its own power. It will cap the heads so they will not dry out as much. If you leave the printer for quite a long time, a few months or so, It may help to carefully wrap it in plastic film but make sure the carriage don't move from parked position. This will help some of the air from getting inside also. I know, it is a bit of a problem but its better to be safe than sorry. This may or may not help anyway, just an added precaution.
It's not the cartridges you have to worry about! They seal themselves (or most do). It is the printer heads that will clog if left unprotected for just a short time. Good luck and have a nice vacation. Don't worry about the printer if you have protected it this way at least until you return! Hopefully everything will be fine.