Does the umbrella cloth (or whatever material it is made of) act as a filter and modify the original color temperature of flash?
Most umbrellas I've seen are white or silver to maintain whatever color is directed at it. So if you gel your flash it should be relatively unaffected by the umbrella. However, if your umbrella is a different color, then that would affect the color of the light hitting your subject.
Or think of it this way, the umbrella material is often like those 5-in-1 reflectors. Silver on one side and gold on the other for certain effects, or a scrim to soften the light, but maintain the natural color for the scene.
Short answer: It can, depending on the color of the umbrella.
If the umbrella is a neutral color then the color of the flash will be unaffected. Neutral would include black, grey, and white. The various wavelengths of light that the flash emits will all be absorbed by the umbrella in equal measure. If the umbrella is any other color, such as gold or silver, then certain frequencies of light emitted by your flash will be absorbed in greater amounts than others, and the color of the flash will be modified. This is the case whether shooting through the umbrella or reflecting off of it and is also the case for any other maetrial the light passes through or bounces off of, such as walls or ceilings.
I think it can vary by the quality of the umbrella too; more expensive umbrellas often use better fabrics that avoid altering the colour of the lightsource, whereas cheaper umbrellas can alter the colour because of cheaper fabric used. Obviously this isn't a hard and fast rule, but if you're choosing an umbrella, it's worth bearing in mind