With underwater photography one of the biggest problems you face is backscatter - light being reflected back from the flash into the lens. This is most common in areas where there's a lot of sediment carried into the water from runoff or river sediment, but it can still be a factor in places without significant rain or river influx.
The way to avoid backscatter is to limit the amount of light coming straight back into the lens (ie use a diffuser) or set up your gear in such a way that the primary light source (for instance a remote strobe) angled so that light hitting the bits of sediment is reflected away from the lens. This is why you see underwater cameras with strobes on arms set away from the camera body, rather than tucked next to it.
However you then have the problem of getting the remote strobe to fire when needed. DSLRs will often have TTL cable ports built into their housings, so the camera's metering system can take charge of them, but the smaller cameras won't have that functionality.
Strobes built for these are designed to be fired in a slave mode - when the camera's internal flash fires, they detect the light flash and fire in response. You may (depending on the conditions) find that the internal flash itself doesn't produce enough light to trigger the external strobe. In that case you can buy fibre-optic cables that link the internal flash to the external strobe. These will increase (although not guarantee) that your external strobe will fire when needed.
So the short answer is that while you can theoretically remove the diffuser, in practice you risk getting too much backscatter as a result. An external strobe is not essential, but will help you get much better results, much more reliably.