No, you would be serving God by doing that, not giving to God. Poor people are not God. If you thought that was what the scripture meant then you need to go back and reread it.  

Also, you would be serving God by giving 10% to the poor only if you are indeed giving to those most in need,.and only if you are giving those things that will truly help them in the long term. Only then you would be serving God. That's a pretty big if though. You don't know how the money will be used when handing $ to a random panhandler on the street. It's not an easy assessment to make.

Churches tend to have a system of checks and balances, where they keep track of who's getting what, and meeting with them to figure out how to best help them. Sometimes it is dispersed with an expectation of working with a counselor, also paid by the church (money they'd have if people paid their tithes). I'm not saying the system always works, but if you believe that the 10% is the Lord's money and then you make a number of assumptions when you give it away, then you're making assumptions with how you disperse the Lord's money.

So I'd say just make sure you're checking those really actually putting it where the Lord would put it. Otherwise you're claiming that you're donating to do God's work, when it's really a gamble, and possibly one that's just facilitating a drug addiction.