Hello Udari, It is totally depending on person to person. Many people succeed because they keep fighting until the end. If the person thinks positive he will get something positive. Depression is the thing that happens with everyone. But for this, no one should be stopped. Depression is part of life. Rather the person should think about the positive scenario. The advantage and disadvantages of it.

Yes, I think a depressed student can study abroad alone. I also felt so much depressed while doing my Ph.D. in abroad. I saw this happens to everybody. There are so many tips to fight with depression. A depressed person should help his own self to get out of it. Also, keep exploring the good side of studying abroad and the result of being patient. 

Good Luck.