Certainly is. You can use CSS in Chrome:
console.log("%c hi", "background: url(path/to/your/icon.png) 0 0 no-repeat; padding-left: 20px;");
From the documentation:
Dev Tools supports the following format specifiers:
%c Formats the output string according to CSS styles you provide.
Caveat:
The console doesn't support background-repeat for some odd reason. So you'd be better either adding some padding to your icon, or else moving the icon to the right-hand side:
console.log("hi %c", "background: url(path/to/your/icon.png) 0 0 no-repeat; padding-left: 20px;");