As jl2012 said the answer is no. The same keypair can be used on both networks but they will produce different addresses.
key: b7b0dcb8cdca3f9a6377cb0f1f5942cec1b3c0f4d6d03dabceced635209aefe1
pubKey: 03e0c6de6ab1c298125368df9973cab1811620cf8349834308acce82dd5ac26419
pubKeyHash: 379800c38269d88e850721399a90e81e91d9eea9
mainnet address: 164xFuP2uhrJX8eVP77k6rrDfboNo21hRR
testnet address: mkauYxU1ijHZJF876g67vn4YXbQ5kASPut
For obvious reasons please nobody use this example key for anything.