No, it really can't, because like I said, you're confusing your light and filter properties. You can shine the whole spectrum through a red filter and it'll never come out white.

Now, in ideal situations, shining a red light, and a cyan light in the same place will yield a white spot. Filtering white light through a red filter, then a cyan filter will result in no (zero) light passing through. Shining cyan light through a red filter will result in a lavender color.