I understand that in general a List is not thread safe, however is there anything wrong with simply adding items into a list if the threads never perform any other operation
This would cause problems, as the List is built over an array and is not thread safe you might get index out of bounds exception or some values overriding other values, depending on where the threads are. Basically, don't do it.
There are multiple potential problem... Just don't. If you need a thread safe collection, either use a lock or one of the System.Collections.Concurrent collections.