Yes, that's possible. I also don't have an idea how to prevent this. I guess that risk is a bit lower on Discord, as you need an account there to accept an invite - but I assume a malicious person could create multiple Discord accounts to do the same.
The use cases for this functionality are probably quite limited, but as I was going to add the batch link creation today anyway, and @reggaemuffin requested this particular feature this morning I figured I'd just add that option too.

One simple security measure could be storing and showing the IP addresses of the requesters,  so a malicious user would need to put at least a bit more work in. Right now the only indicator would be the timestamp. There's no way to make it "safe" though (if you have further ideas, they're welcome!).