Technically no, not yet, but something may come in the future using Uri Schemes.
For now, it seems that you can only run the WhatsApp app by doing this:
await Windows.System.Launcher.LaunchUriAsync(new Uri("whatsapp:"));
but on iPhone, you can use this form of Uri
whatsapp://send?text=Hello%2C%20World!
so I expect the same functionality to appear in the near future in WhatsApp for Windows Phone. There's no reason why they wouldn't implement it.
In fact, maybe they already have, but I haven't found it publicly documented. See on Nokia Developer website for other Uri Schemes
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