No, but even modern GPUs can run in BIOS and VESA compatibility modes without drivers, which DOS does support. You just won't be able to use hardware 3D rendering.
It's not even VESA. DOS just uses the VGA 80x25 character terminal mode that all x86 computers still have to start in for backwards compatibility, where "video memory" is mapped to 0xb800 in the 1MB real mode address space. Software you run can then change the video mode, such as to a VESA mode if supported, or for ultra nostalgia, "screen mode 13" (320x200 256-color mode).
You could also just use a VGA or DVI to HDMI on a compatible card which supports DOS, you'll have to pump in external sound but that's already the case on Most Dos machines who's soundcard is external, and since DOS and its software library doesn't exactly support modern soundcard standards.
Lgr did a video 6 years ago where he threw Ms dos 6.22 onto a modern gaming PC just for the hell of it. It has some issues with booting but he it ran. PC specs were a ryzen 5 1600x with a 980ti. And at some point in the video you can see on the monitor he's using that it was using HDMI.