Hi, yes, it should continue to be ok.
Of course there will be minor variations, even between successive prints. But these should not be noticeable to the human eye, even if the instrument can detect slight variations. In fact, if you take multiple readings of the same prints, you'll probably find a slight discrepancy here and there; it's not unlike using a densitometer on a negative - you might read a test patch at 1.51, but the next reading is 1.52; it's "on the fence," so to speak, and might fall either way.
Probably the best way for a photographer to keep an eye on things is to have a "standard image," and to make an initial reference print. If you ever think that something is amiss then make another print and compare critically against the reference. In our business we did all portrait work, so we used a portrait-type of image, including a Macbeth color chart; this allows spot readings if you want to check. (I'm presuming that the ColorMunki allows this; my experience has been either with i1 Pro units or a couple of automated strip readers.)
As a note, if you DO find noticeable color changes with a new set of ink cartridges this is a deficiency in the maker's quality control, not something that you should be expecting. FWIW, I don't know if the Munki software allows it, but the fancier software packages allow averaging multiple sets of target readings, so if you had several different (same model) printers you could average all and make a single color profile that is a "good fit" for any of them, and this would sort of accommodate production-line variations.