Simple answer, yes. Simply because of the grain orientation. they will tend to be fragile. Think of it the same as a 1-2" Cookie cut from a log. It's pretty weak compared to a long grain board. Drop it on the floor and there is a good chance it will break.
Putting a long grain border around it is not a good plan, it's almost certain to crack due to seasonal movement. Traditional end grain butcher's blocks are made thick, 6" or more, so there is some strength in the wood to resist splitting.