To answer the original question:
No.
It's ATC's responsibility to listen for correct readbacks and chase if required. Various methods are employed to ensure this. E.g placing a tick next to the SSR code/level/route/heading, etc on a paper flight progress strip, or sometimes placing a < next to the instruction in Eurocat.
As mentioned above, it's more of a problem if you read it back correctly and then make an error in carrying out the instruction.