If the basis of f.lux and copycat programs is that blue light keeps you awake, then could I be more focused during the day if I have a blue rgb light strip (provided the room is fairly dark, like when it is overcast) ?
f.lux works like this: at the end of the day (sundown), sunlight contains decreasing proportions of blue light. This lack triggers the production of sleep hormones like melatonin.
In the morning, sunlight triggers the 'wake up' routine of the body. This can be simulated with bright light (a.k.a. winter depression therapy). This light can be full-spectrum or blue, and it has to be bright: 10,000 lux full spectrum, i.e. way brighter than your normal sitting room lighting. It has to simulate sunlight on a clear day. You can get purpose-built lamps for light therapy, no ordinary lamp is bright enough.
Note: if you suspect you have a winter depression (Seasonal affective disorder), see a doctor.
Adding extra blue light in the middle of the day doesn't accomplish anything.
There are alarm clocks ('Wake-up light') that include a light to simulate sunrise. These are effective because they help you wake up gradually, instead of rudely interrupting your sleep. They are not meant to treat winter depression, and are not bright enough to be used for that purpose.