[NOTE: I answered this question without realizing that it was not for Canon BCI type cartridges. Please apply the answer as it fits for the HP cartridges.]
It depends on where you made the holes. If you made them into the reservoirs, then you will definitely have to seal them air tight. Otherwise, as soon as you remove the clip off the outlet port, all your ink will drip out. Or, at least, it should drip out. If it doesn't, then something's wrong. In fact, this is the way to test whether there is a leak in the reservoir and is a good test to perform even on a new off-brand cartridge since some of them have been known to be defective in this regard. In other words, on a brand new cartridge, when you remove the tape over the air vent and then remove the orange clip (make sure you do them in that order), if ink continues to drip out the outlet port, that means you have a leak in the reservoir side of the cartridge.
If you made the holes in the sponge part of the cartridges, then the reason to seal them is to keep the ink from evaporating and tape would be good enough. The air vent hole in an OEM cartridge follows a long winding path before it reaches the atmosphere which makes it very hard for the water vapor to escape from the cartridge. An unsealed hole directly into the cartridge will not affect the operation of the cartridge and it will take a long time for the evaporation to result in a color shift of the printed ink, but this is the reason for the design of the Canon cartridge.
Fading of patch sheets in the dark