Will a tall multi-tier plant stand block light to the lower shelves?

Yes, this is the single most common complaint in specialist houseplant communities. Threads in r/houseplants repeatedly note that on staggered or ladder-style stands placed near a single window, only the top two or three pots get usable light and lower plants etiolate. Either pair a tall stand with supplemental grow lights, place it perpendicular to the light source rather than against a wall, or choose lower-profile two- or three-tier designs if you don't want to add lighting.