TL;DR
Yes, on low heat only. High heat and fabric softener both wreck the split fibers that make microfiber effective at trapping dust.
Microfiber towels and cleaning cloths work because their fibers are split into thousands of tiny strands that grab dust, oil, and moisture far better than cotton. That same fine structure is also what makes them sensitive to heat in the dryer.
People who dry microfiber the same way as regular towels often end up wondering why it stopped picking up dust as well. The answer is almost always heat or softener buildup.
What heat does to microfiber
Microfiber is typically a blend of polyester and polyamide, both synthetic and both sensitive to heat. High dryer heat, generally anything above low or medium-low settings, can melt or fuse the fine split fibers together, permanently reducing the surface area that makes microfiber good at trapping particles in the first place. Once fused, that damage doesn't reverse with washing.
Fabric softener and dryer sheets are the real enemy
Liquid softener and dryer sheets coat fibers with a waxy residue designed to make regular fabric feel silkier and reduce static cling. On microfiber, that same coating fills in the tiny gaps between split fibers and kills the static charge that helps it grab dust, turning an effective cleaning cloth into one that just pushes dirt and streaks around instead of lifting it.
The right way to dry it
Use a low heat setting, or air dry if you have the space, and skip softener and dryer sheets entirely, every single time, not just occasionally. A low, no-heat, or air-fluff cycle is usually enough to dry microfiber towels within an hour or so without damaging the fibers, and air drying on a rack works just as well if you're not in a hurry.
Washing habits that protect it
Wash microfiber separately from cotton towels and other lint-producing fabrics, since microfiber's static charge actively attracts lint during the wash cycle, which then clogs the fine fibers and reduces their cleaning power over time. A mild detergent without added softeners, on a warm or cool cycle, keeps the fibers performing at full strength for the longest stretch.
Signs it's time to replace them
Even with careful washing, microfiber cloths eventually lose effectiveness after dozens of wash cycles. If a cloth streaks glass or leaves lint behind instead of picking it up, it's worn out rather than dirty, and no amount of rewashing will restore it. Most microfiber cloths still perform well for 300-500 wash cycles when cared for correctly, which for a daily-use cloth can mean well over a year of service before you need to think about replacing it.
Microfiber survives the dryer fine as long as the heat stays low and the softener stays out. Treat it differently from regular towels and it'll keep grabbing dust the way it's supposed to.