It might spend more time pushing pixels around since 4k is 10x as many pixels as 1024x768, and I'm not sure if single-threaded processese that are memory-intensive are 10x faster.

TQt3 (TDE's Qt3 fork) uses X graphics primitives and the X render extension (if available), both of which are hardware accelerated on modern Xorg via GLAMOR (OpenGL-based 2D graphics acceleration) - at least for the open source drivers which are part of Xorg (i don't know if Nvidia's proprietary driver uses it but chances are if not, they're using their own 2D accelerated graphics anyway), so it shouldn't spend more time pushing pixels around than anything else that uses a HW accelerated API.