Depends on the error as to how it will affect you.
The 2 most serious ones I’ve seen are:
Self test error or communication error
Both will cause long post times. Once up and running if you don’t use Ilo you won’t see any difference.
There’s a less serious nand issue that won’t slow down post. All of Ilo will function pretty much but you lose intelligent provisioning functions and some other small things. You get a warning in Ilo. This can sometimes be fixed with Ilo update and nand reset but doesn’t usually work.
From my personal point of view, ilo is one of the big reasons to use these servers. If you don’t need / use out of band management then there’s likely better options. I would avoid any with Ilo issues.
With that said, if you get a good deal on a server then the system boards are becoming more common in a lot of cases so swapping that out might not be problem.
With the price of ssds what they are now for a small 100gb why bother with the additional setup and potentially failure points.
I’ve run esxi through network and even that wasn’t fun with longish boot times. I certainly wouldn’t like to run proxmox that way. These days there’s really no reason not to have “some” fast direct storage in each server even if it’s just used mainly as cache.
What you’re looking for is possible but to me the saving of $20 ish per machine just isn’t worth introducing more headaches.