I use the terms "strobe" and "flash" interchangably, so I think what you're asking is can you use an "on-camera" flash (or even the built-in flash) as opposed to an off-camera big flash (or strobe) system, and the answer is yes, that's exactly what I use. On the shot I posted, the flash was a Nikon SB-26 sitting right in the hot shoe of my F100 (film) camera, set to manual mode and attached to an external battery pack (Quantum Turbo). I don't know if a built-in flash would be powerful enough to do this and get decent settings. I have used an off-camera system (Norman 400b with umbrella) on other shoots, but this system seems to work fine for me and travels really well and light-weight.
To do it, I use a flashmeter (and someone to hold it) to meter the flash falling on the model (incident mode) from whatever distance we're at, using about 12-15' from each other. That't where I set the f-stop on the camera (usually f4 or f5.6), and then I use the camera's internal meter to read the sky (without the sun) to get me a sky reading (usually 1/250th or 1/125 until the sun sets) for a saturated look like that image. Then I shoot it at those settings, sometimes slowing down the shutter speed to get a brighter sky or water. Most important, make sure the distance between you (hold the camera with the flash) and the model doesn't change (gotta love zoom lenses!) If it does - if she gets knocked around by the ocean - re-meter. I suppose some people will advocate doing this all with auto-settings on the camera and strobes, and they can check the results in their LCD screens, but I have't played with it that much and I don't usually trust auto-anything, and I am shooting film, so I do it all manually and I rarely screw it up.
(Same beach in Florida, same camera & flash, different model, two years earlier than the other shot. This one is Maiki).
As for the gel and flash thing.... No, you can't easily fix it on PS. Since I don't think you can change the color of the flash post-exposure, you need to do it at the time you shoot. (Besides, you'd have to "select" the whole model in your shot each time). If you were to make an overall color change either by filter on the lens, or doing an adjustment in PS, the entire image would shift - the sky and water as well, and the model would still be proportionally cooler than the rest. If you put the gel over the flash, the warm gel is only affecting whatever the flash hits - in this case the model - while everything else is exposed by the shutter speed and comes forth with its natural coloration, in this case, the very warm sunset. (I don't think you can change the white balance of a flash seperate from the camera, but if you could that would work). The gel will cost you almost a stop in exposure, so you do need a powerful flash. Check my reply to djyeo80 to learn about the gels.
Andy Pearlman Studio