Most brokers allow odd lots, but I have found that the fills you get are not as good as you will get if you trade > 100 shares.
You will not find odd lots < 100 shares on the time and sales tape. They dont have to be reported and a limit order for < 100 shares will not move the national best bid or ask.
Also, most brokers have minimum charges, so your cost will be much higher on a per share basis.
Still, not a bad way to test execution logic. When I take a new system live, I usually start with small positions, a few $k or so and intervean if needed until I get the logic worked out.