Not quite. You test the null hypothesis...that there is no relationship. If you can reject the null hypothesis, that means that it is likely the alternative hypothesis is correct. In other words: you don't test to see if your idea is supported, you test to see if the opposite of your idea is supported.
Falsifiability simply means that conditions exist under which the proposal could be proven wrong. There are any number of observations that would prove evolution wrong. The classic is a rabbit in the pre-Cambrian, but others would be things like a dog giving birth to kittens, or a pig with wings, or a dog with scales...any kind of true chimera.
You seem to be under the misapprehension that hypothesis testing can only occur in a lab. That's ridiculous...unless you want to say all of astronomy is false because it's never been tested. For cases where direct experimentation cannot occur, testing takes the form of observation. No observation that contradicts the general theory of evolution has yet been made. Some parts of Darwin's original theory have been demonstrated to be incorrect, and other ideas have come and gone, but that species change over time and that all life on earth shares a common ancestor? Nothing to contradict that has been found and plenty of evidence to support it has.