Possible to permanently destroy a logic board or the ram slot?
The short answer is yes (POSSIBLE - but not very likely, in my experience)
more likely a kernel panic, or black screen, or error beeps, or a flashing power light on those Macs that still have a power light - but not permanent damage...
Then, I have most often seen memory fail when first inserted. Outside of that, I have had failed logic boards (bad memory controller, or the slot might be physically broken) causing the RAM chip to fail.
But, when a RAM chip is bad, it's bad, and replacing that RAM card usually is all you need to do, along with making sure that the card is seated properly.