Direct answer
No. A boundary doesn't need approval to be valid. It can displease the other person and still be legitimate, because the validity of your choice can't depend on the satisfaction of whoever receives it.
Approval and validity are not the same thing
A boundary doesn't have to hurt the other person. It can be said with care, without aggression, without coldness. But avoiding harm is one thing, and making the boundary's existence conditional on the recipient's contentment is another.
When you wait for approval to feel at peace with your own choice, the boundary has stopped being yours. It now belongs to the other's reaction. And as long as that reaction doesn't come in the tone you hoped for, you keep reopening the negotiation.
What self-knowledge has to do with it
Learning to hold a decision without turning it into a defense is the work of identity. It's recognizing who you are and trusting your own experience without continually depending on external confirmation. The other person's satisfaction is theirs. The legitimacy of your choice is yours. Keeping these two apart is what lets you not disappear inside every hard conversation.