Yes you can. There is nothing in Zebble that prevents you from using the native APIs directly.
For custom http calls, I recommend using the HttpClient class which is by default available in all 3 platforms of a newly created Zebble project.
For Device APIs, you can of course use the standard API classes of each platform, but to save time and achieve 100% code reuse I strongly recommend using the http://zebble.net/docs/device-api. For example if you want o use the lamp (aka flash, led or torch) you can very easily implement that on all platforms with very little code code:
// Determines if a lamp feature is available on the device.
if (await Device.Torch.IsAvailable()) { ... }
// This will switch the lamp on.
await Device.Torch.TurnOn();
// This will switch the lamp off.
await Device.Torch.TurnOff();