you'd pick this up straight away, ECC ram detects memory errors in real time. The reason why you run memtest is to systematically go through all the bits and flip them in a known pattern.
You can check that known pattern to see if the bit changed properly.
With ECC this is redundant, as each byte(or word, or some unit of memory) has a hardware checksum. So using ECC ram in normal operation will indicate if there are errors.
The reason to run memtest on ECC memory is to verify that every bit of memory is good before you finish building the system, installing an OS, and putting it into production. If you have, say, 32GB of memory, there's no guarantee you'll hit those bad bits for ECC to log an error until you're doing something memory intensive two weeks later.
The primary use case of ECC is to handle random bit flips from cosmic rays and whatnot, not to mitigate bad hardware. If you have bad memory, replace it, don't rely on ECC. The only way to test memory is to run something like memtest, where you read and write from every bit in memory.
If you're OK with finding out a month later that ECC is logging a hundred uncorrectable errors an hour whenever you do anything memory intensive, then sure, don't bother memtesting. If you would rather deal with it beforehand, then run memtest.
Yes, but again, you may not get that alert and find out that memory module is bad until months from now. It all depends on where the chip is bad at, how much is bad, how much load is usually on the system, etc.
I (and I would guess most people) don't want to find out a month (or more, potentially much more) from now that the memory module is bad, I want to know now so I can RMA it and get it over with without having to take a running system down and apart.
That's the problem that memtest solves, ECC does not solve the same problem at all.
You can check that known pattern to see if the bit changed properly.
With ECC this is redundant, as each byte(or word, or some unit of memory) has a hardware checksum. So using ECC ram in normal operation will indicate if there are errors.