Maybe. That is about the best answer I could give you. In general, weight gain is determined based on a lot of factors such as your body composition, metabolism, the calories you actually eat, the exercise you do, the time spent doing it, your current health etc.
Assuming you are a young healthy young male its possible that you could put on weight/muscle doing this program. It's also possible that you could lose weight/muscle depending on how you do it and the calories you take in. If you do a google search and look up Riptoe starting strength then you would have a very good program that will likely increase your weight, strength and muscle gain. The question is why is it important to just put on weight/muscle? Ultimately what is your goal? Bodybuilding? Improving your looks? A sport?
Most guys your age have a desire to put on muscle and most of the reasons can be summed up in few words. 9 times out of 10, because of the media you are exposed to, its a desire to look good and impress those around you. We all have that desire at some level. Nothing wrong with that necessarily but it could put you on a road to failure if your not careful. The media pumps out the ideal man/woman everyday on magazine covers, television, radio etc. The only problem is that sets up 99.99 % of the rest of the population to feel inadequate. It's sad really because at some level we all fall victim to it because there is so much exposure.
At 15 years of age you have a prime opportunity to develop your body and mind into something beyond your expectations and likely beyond anyone elses. I would recommend you take a hard look at your reasons for gaining weight/muscle then change them. Ultimately you are going to age and unless you make a career out of bodybuilding real life issues are going to outweigh the desire to put on weight/muscle, you are going to blink and be 25, blink again and be 45, blink again and be 65. When you look back at your life what will you have accomplished? Some weight gain and muscle? Doesn't seem so important from that view does it?
I can tell you from personal experience that at 15 I thought the ideal man looked like Arnold Schwarztawhoever and I wanted to emulate that ideal. I spent years lifting and stuffing down calories with one failure after another. I studied sports medicine, became a physcian assistant, and read a lot of books about nutrition, exercise, weight lifting, bodybuilding etc. What I learned from all that media hype is that its pretty much all bullshit.
I recommend going an unconventional route and work on developing your body to do strenuous functional activity that you may actually need to use in every day life and help prevent you from getting early onset disease. If you set your mind to achieving multiple goals and working hard for those goals you will be pleasantly suprised one day when you look in a mirror and noticed you look better and have muscles. You see, the looking good part part is icing on the cake but is not the important issue. It will make you happy for a time but once you have it then what?
Setting goals physically and mentally that are challenging that make you actually struggle to achieve them are a necessary part of the human condition to build your character. Simplefit can start you on that path. Since you don't have a gym and I'm guessing you haven't really been involved in a lot of school sports this is an excellent program for you to get started with. However, I would also recommend doing school sports also as you get a free coach :).
I wrote an article on some of the Crossfit recommendations and I highly recommend you go to their website and devour all the free knowledge they have to offer. Here is my article viewtopic.php?f=7&t=2166
Just some food for thought. Im 48 years old, 6 foot tall and weigh around 190 lbs. I don't look particularly muscular at least not for a muscle and fitness magazine, and I can pinch an inch on my waist. But I've been following the mantra I'm preaching to you now and I can compete with most guys in their 20's on the Simplefit exercises and actually outdo most of them. Thats a good feeling because I know I'm heading down the right path. My goals currently are to complete 50 pullups without stopping, 100 pushups without stopping, and all the other Crossfit goals to include the hero and girl workouts as Rx'd. In my quest for that I've lost 30 lbs of fat and gained almost 10 lbs of muscle.
You can easily surpass that because you have the advantage of your youth and are in what we call the "Prime" for achieving these goals. At no other time in your life will you be able to make the gains in strength, endurance, flexibility, agility, speed etc. that you can now. Take advantage of it and work hard. You will never regret that decision. I promise you.