That would be unconventional. Now, nothing is necessarily taboo -- if you like the look, go for it. It's certainly not common, but mixing lighting is a creative or artistic decision. And some cameras (like the Red One) perform better under daylight fixtures than they do under tungsten.
Using a straight-up daylight key and a tungsten fill won't look "normal", but you'll have to decide if you like the look or not.
I've frequently lit daylight key & fill, but a tungsten hair/rimlight. Not always, but sometimes I like the warmer glow, has a bit of an angelic look. And when lighting with daylight key/fill, I frequently like to use a light straw gel to warm the image up some. That would be about the same thing as lighting with a tungsten fill but using maybe a 1/2 CTB on it to close the color temperature gap...
If you're going for a conventional look, don't mix color temperatures. It would be for a specific look or purpose.
I love it (for a look) Camera on daylight, we have uncorrected tungsten, daylight flouro, white LED and a tunge with a red filter, not to mention some green instrument lights..
In the image examples, it gives you a good sense of when mixing color temps is effective for what the scene is trying to show (or at least what I am imagining the scene showing)
He is in some sort of work area, where lighting is always mixed, so the contrast between the color temps on his face gives the light a motivated quality, even if its technically an unmotivated light. Just sort of adds to the mise en scen your working with.
But nothing is taboo. Are you asking if you can mix temps because you don't have access to the same color temp lamps? If so, I'd just gel whatever light didnt temp out around 5200, so your even across the board (if thats what your even asking)