There might be a few rare souls in publishing who would offer encouragement based simply on age. But this is not therapy nor is it English Comp 101. It's a business where the editors/agents are looking for product they think will make money... If your manuscript is marketable and they see a profit potential, they will find a way to make it happen.
I can't help but think you are overlooking something. You say it's about marketability and profit potential, and yet completely ignore the money spinning potential of a young writer?
I'm not going to deny that at the end of the day, the manuscript is paramount, but neither am I going to deny that the author themselves is just as much of a product as the book they are selling. Authors that have an interest angle (e.g. young age, or unemployed single mother) are often pushed into the public eye. It's free publicity, and publicity helps sales.
Most, if not all agents are aware of this potential when considering a manuscript from a young writer. Sure, some might groan when they see it in a query, but this is because most young writers (and most writers in general) that submit to agents aren't very good. They won't throw down your query in disgust just because you dared to mention it, and if they do, well... tough. I'd imagine most will keep this tidbit of information at the back of their minds and go on to read sample pages just like any other submission. If they like those pages, and end up loving your whole manuscript, then the interest angle is only going to persuade them further.
Now, I'm not saying that telling an agent you're a young writer will automatically get you an offer of representation regardless of the quality of your writing. But still, you never know if the marketing potential might help persuade an agent. They are, after all, sales people.
At the same time, if you have a fantastic manuscript, then chances are they will pick you up regardless of your age. But if you have a 'great' manuscript, and they've seen four other 'great' manuscripts that week, who is to say that the prospect of helping a sixteen-year-old become the next Big Thing won't be enough to sway them to your side over the other four candidates?
We live in an image conscious world after all. It's no longer just about the book, it's also about the person behind it. Zadie Smith and Christopher Paolini are both writers that might never have had the same success if it hadn't been for their youth. Very few people think they are absolutely fantastic writers, but nevertheless having an interest angle helped pushed them into the spotlight, where they have since flourished.
Just my two cents. All in all, I'd say there's no harm in using anything you can to your advantage. It's a cut-throat business, so why not? Just don't make it obvious.
