Will there be any difference?
There might be. Most light sources, including tungsten bulbs and photographic strobe flashes, output fairly broad spectrum light. Their light may be centered on a certain color temperature, but their total outputs generally include components from a much broader range of the visible spectrum.
- A tungsten bulb outputs light that is most heavily concentrated at around 3000K, but there is some light from pretty much the entire visible spectrum included in lesser amounts in the output from a tungsten bulb.
- A photographic strobe outputs light that is usually most heavily concentrated at around 5500K-6000K, but there is some light from pretty much the entire visible spectrum included in lesser amounts in the output from a strobe.
Depending on the exact output of a specific source of tungsten light and the exact output of a specific strobe at a specific power level for a specific
'pop' (because the color and distribution of the wavelengths of light from a strobe can vary by the power level/duration to which it is set and will even vary to one degree or another from one shot to the next when set at the same power level/duration¹) you will likely get very slightly different results when using either one and setting your raw converter to a generic "Tungsten" setting or a generic "Strobe" setting.
Which one will show certain features of the skin more or less than the other will all depend on the differences between the exact color profile output by each of the lights compared to the exact color profile applied by the raw converter for each type of light. Most raw converters are flexible enough to compensate for such differences and in practice you should be able to create the same final image using either source of light if that source of light is the only source of all the light captured in the photograph.
¹ This is why professionals are willing to pay big bucks for studio strobes with very consistent output from one shot to the next and from one power level to the next. It makes their job in post processing much easier when the output from their lights is more consistent from one shot to the next.