In my experience branching euphyllia are very hardy when it comes to fragging. I have cut several frags for people right then and there and all have done well. However, they are so susceptible to brown jelly I would let them heal if at all possible.
I presume you mean if you cut the branch/stalk. If so, no. In my experience it's old bones and I've never seen any issues with breaking/cutting it anywhere. I've cut many of them and only if I break the mouth/head do they require time to heal.