HDMI covers a range of screen sizes, the latest standard goes up to the 4K standard, earlier ones managed only 1080p and 1080i modes and below. HDMI is adaptive to the screen to which it is sending image data.
HDMI also carries sound data.
To answer your question, yes, unless you have high definition screen, in which case the picture will show, but at a lower resolution than the screen is capable of
You can get HDMI-VGA cables
for example:
https://www.amazon.co.uk/d/HDMI-Cables/Converter-Adapter-Support-Monitors-Projector-Loop-HDMI-VGA-1-8m/B01N3OQBAD
Check the resolution of your screen, and that the cable will give the required resolution before buying.
I'm pretty sure the VGA Sub-D connector is limited to 1680x1050, which is slightly worse than than 1080p or 1080i (1920×1080). but not as good as 4K.
To be honest, you probably would not notice the difference in image quality, but it's best to give you the full answer, rather than simply saying, "yes, it will be fine"
Hope it helps