I would advise to consult your client on the matter as this is a situational manner. Though, if you are looking to try something out I would recommend a very subtle drop shadow under the navbar to help distinguish it. Though the color alone would do it and it seems lately that flat design is becoming a bigger trend.
Also, I would advise against the gradient in the navbar. The navbar is one of the, if not the most important element on a website. You do not want to make it hard to read or anything in that manner. The only exception to this is if your navbar is needed to look like it has volume. Still, it would need to be subtle. So all in all, best practices would be to consult your client on the situation, take in their opinion, use the best course of action and go with it.
Also it doesn't hurt to try different variations of this layout and look to give your client options.