Yes, Autograd tracks the indexing operation as well as additions, so your model should get valid gradients as shown in this example:
x = torch.randn(1, 6, 4, 4, requires_grad=True)
x0 = x[:, :3]
x1 = x[:, 3:]

x0.mean().backward()
print(x.grad)
x1.mean().backward()
print(x.grad)