Yes you can run that setup, and a whole lot more -- up to five large displays (but at that rate the fans would likely spin up).
The Studio Display is "only" a 5K display -- the Studio Mac can run four 6K displays, PLUS
an HDMI display up to 4K at 60 Hz (the limit of high-speed HDMI cabling).
Video Support
Simultaneously supports up to five displays:
- Support for up to four Pro Display XDRs (6K resolution at 60Hz and over a billion colors) over USB-C and one 4K display (4K resolution at 60Hz and over a billion colors) over HDMI
Thunderbolt 4 digital video output supports
- Native DisplayPort output over USB‑C
- Thunderbolt 2, DVI, and VGA output supported using adapters (sold separately)
HDMI display video output
- Support for one display with up to 4K resolution at 60Hz
- DVI output using HDMI to DVI Adapter (sold separately)