I know you mean well, but you do not understand what you say. In order for BTC to ever help anybody, it needs to first be adopted by people who will actively develop it as a useful tool. Sorry, but that excludes every homeless person I have ever known. I am sure you could hunt down one or two homeless people who would actually start some sort of business or organization based on bitcoin if you gave them $100 of it, but personally, I would bet on the student having a better chance at helping to grow the network.

Where could a homeless person even spend it? Seriously, you would not be helping anybody at all if you did that, and, in fact, you would ultimately be hurting the bitcoin network growth and indirectly harming the homeless people by stymieing any sort of benefits that bitcoin might have ever been able to give towards wealth equality.

Give the homeless person $100 if you want, but don't do it in bitcoin. We aren't even close to the point in time where that would be helpful for anybody except to make you feel better about yourself.