I've had laser printers give me trouble-free printing even if they've been sitting there for months at a time. Toner is basically dry powdered ink, so it's not going to fail the way an inkjet printer would if you don't print for several months at a time. As long as it's not exposed to excessive heat or humidity, toner has an indefinite shelf life.
That said, imaging drums can degrade over time. While this is something in the ballpark of several years, like toner, it can degrade faster if it's stored in an excessively hot or humid environment. Of note is the fact that by its very nature, the drum is photosensitive: a drum can be damaged by excessive exposure to ambient light, such as by leaving it outside the printer for more than a few minutes without covering it with something opaque. But if it's properly cared for and assuming it isn't worn out through normal use, the drum should last at least five years (from my experience with Brother laser printers, which have separate toner and drum on all models), so it shouldn't be an issue.
The Canon Color imageCLASS MF644Cdw has the toner and drum integrated into each cartridge. This means that whenever you replace a toner cartridge, you're also replacing the imaging drum for that color. This should mitigate issues with drum degradation, as it's unlikely that any particular cartridge will be in the printer for an extended period of time. (Most Canon laser printers use this cartridge design, known as the Single-Cartridge System. The idea is to simplify management and replacement of supplies by not having to deal with separate drums or waste toner containers, though cost per page may be a bit higher.)
The fuser and transfer belt (monochrome laser printers use a simpler transfer roller), which are often consumable supplies on high-volume printers and copiers, are designed to last the life of this printer. These parts are subject to physical wear and tear during use, but do not degrade appreciably in storage.