it absolutely does matter with the pixma ip3000/ip4000/ip5000 series. i dont know about their other printers, but i still use these models as they dont use chipped ink.
from what i can tell, leaving the printer prevents clogged pintheads by keeping the ink warm at the head. im not sure if that theory is true or not, but it does work. case in point- i just moved. i had my canon ip4000 working PERFECTLY with the printhead nozzle check patterns for 2 years. i never had a clog and i used cheap inks too. i always left that printer on because in the past i had problems with the printheads and saw suggestions online to try leaving the machine on.
so for 2 years it was perfect, and then it went to the new place. it sat on my desk for 2 months before i turned it back on (extension cords were scarce). guess what? its completely fucked. only the yellow prints, and the large black tank was completely gone from printouts.
i ran hot water over the printhead for a few min, and it brought it mostly back, but the nozzle check patterns still show gaps. and the blue color has now disappeared again. im afraid i might have to buy a new printhead!
i also have an ip3000 in storage for 2 months too, and i dont even want to pull it out now because i know what i will see. that only has 4 ink tanks though, without a pigment ink so its usually a little more rugged.