Short answer: Yes.
For one thing, your own brain is a natural source of levodopa. Not recommended for consumption. And if you have Parkinson’s Disease, then you don’t have enough of it in the first place. But the point is, the levodopa in your brain is exactly the same as the levodopa in your sinemet (or other levodopa-containing drugs). You can’t get much more ‘natural’ than that … simply replacing the levodopa that has been lost as a result of the disease.
Levodopa also shows up in a number of plants and animals. Apparently mussels and other mollusks use it to create the bioadhesive that allows them to stick to things. It’s also involved in the browning of bananas and other ripe fruits (a process similar to the formation of neuromelanin, discussed here). There are a number of supplements available that contain varying concentrations of L-DOPA, commonly based on mucuna seeds, which happen to have an unusually high concentration of it (several percent of their weight). But to put this in perspective, a clinical trial compared mucuna with sinemet, and it took 30 grams of the stuff to get an effect roughly equivalent to one 200/50 sinemet pill (200 mg of levodopa). That’s a lot of mucuna powder. Also keep in mind that the FDA has little power to regulate supplements, and so it is hard to know how much levodopa is really there; it may vary from batch to batch, making it hard to control symptoms effectively.
So seriously … just take the pills.