I don't think it'll be an issue on the Xbox as long as you don't accidentally clear the rendertarget before you are done with it. To be on the sure side when only writing to your color rendertarget, make sure to choose a BlendState which disables color writes to your depth rendertarget. You'll even save some bandwith/performance this way.
E.g. create a new BlendState disabling color writes to second rendertarget:
protected override void LoadContent()
{
this._blendState = new Blendstate()
{
ColorWriteChannels1 = ColorWriteChannels.None,
}
}
Then set this state before you do your draw calls only outputting to the color rendertarget (and reset afterwards):
protected override void Draw(GameTime gameTime)
{
GraphicsDevice.SetRendertargets(color, depth);
GraphicsDevice.BlendState = BlendState.Opaque; // .. or any other BlendState
{.. draws to both rendertargets ..}
GraphicsDevice.BlendState = this._blendState;
{.. draws only to color rendertarget ..}
}