It could be even more dangerous than you are imagining.
If you check a username, then you would probably also be revealing the IP address range and browser referrer that is normally used to access your account.
Google uses IP address and location to help detect illegal access. So giving away this information could make it easier for your account to be stolen.
Of course not. He's going to go botnet shopping and try to log in through a compromised machine with an IP address in the same town, in the same address range.
He might even be able to use the same IP as you, if you happen to be using a gateway with many machines behind it, and one of them is compromised.
If you check a username, then you would probably also be revealing the IP address range and browser referrer that is normally used to access your account.
Google uses IP address and location to help detect illegal access. So giving away this information could make it easier for your account to be stolen.