There's lots of photos of people sitting on them. It just depends on what your definition of cool is. Some people think Harleys while wearing jeans and no helmet look cool and other people think Aprilias while wearing full leather looks cool. It's a pretty plain Jane sort of bike in my opinion so I'm guessing most random people in traffic won't pay any attention to it and most motorcyclists won't take notice either.
If you're 5'9" tall you'll fit on the bike fine though and hopefully your passenger will as well. I've seen two 300 pound people mount a scooter though and it works to get them from one place to the other.
I'm 5'9" tall, but 70 pounds lighter than you. This is me on a Grom, the smallest bike I've ever ridden. I felt like an adult on a kid's bike, but like I said, I doubt anyone in traffic even noticed me.
I ride vintage Vespa scooters which are even smaller (sometimes two up with a passenger) so my opinion probably doesn't match up to yours that well.
In my opinion, the Scrambler is in that same size range of a 'standard' motorcycle like a Harley Sportster, a Ninja 500, a Suzuki SV650, etc... If those seem too small to you, the Scrambler probably will as well.
The only time I've ever ridden with someone that was clearly too big for a bike was a 6'7" tall friend on a 400cc Yamaha twin of some sort. Wide doesn't matter so much as tall does in terms of being able to fit on there.