Yes, this is possible. Someone on Reddit, made a public testnet wallet, from which you could transfer some moneroj to your own address(es), to experiment with (e.g. cold signing, etcetera).
First create your own testnet wallet(s), and then you'll need create another wallet to restore from the mnemonic seed posted in the Reddit article. From that one, you can transfer some moneroj to your own testnet wallet. Please be courteous, and don't drain the wallet.
Note that testnet addresses start with
9, while mainnet addresses start with