Surely is; you'll need to find the config file or where it's defined to whom the syslog is sent to (no, I don't think it's always automatically root, since there could be systems where root account is not used much), and alter the receiver's address from "root@localhost" or something similar (which points to the machine's own root account's mail) to your gmail address.
Be aware, though, that the mail is probably sent unencrypted so if it contains any crucial information that you can't reveal to anybody or everybody, i.e. if you don't like the idea of your neighbours 17-year-old kid ketting his hands on it, don't send it out over the web if you can't encrypt it.
Since syslog may well include some information you don't want to reveal to others, I encourage you to think a way to encrypt the message before sending and decrypt it when you receive it, or drop the idea. You could write a cron-timed shell script to grab the information, encrypt and then mail it, and that's probably a wise thing to do in this case.