Someone is sending me faucet ltc, but I gave them a real litecoin address,
How will it behave ?
Faucet are reward systems that dispenses rewards in the form of a tiny fraction of coins (in your case Ltc) for visitors to claim at certain time intervals which is paid to your real litecoin address.
Will it appear on the blockchain like a real transaction ?
Yes, if the faucet actually paid you then you should see the transaction and you should eventually receive it on your wallet.