Will this picture come out decent quality if printed onto A3 poster?

Nope, it'll likely look really pixelly. If you're grabbing it off the web, it's probably 72dpi (dots per inch) and you need at least 150dpi for it to look good coming out of a printer. And I'll usually go up to 300dpi just to be safe so I know I'll have a super crisp print-out.