It would be possible to grow an albino plant to maturity and flowering in tissue culture or micropropagation. The seedling would have its root(s) cut off and be placed in a nutrient jelly with the right chemicals for growth. As long as the jelly was not allowed to become contaminated with bacteria and fungus and the seedling was given fresh jelly when needed it could be grown long enough to flower.
However, unless the seedling was able to develop some green pigment as it grew older it would not be able to survive without the nutrient jelly. For some specific mutations the green chlorophyll pigment is lost when there is high light intensity but can be made in low light intensities. Sometimes those particular mutants may survive after they have greened in low light.
Without nutrient jelly (or attachment to another plant - sharing resources) to provide the fundamental food for plants (sugar) a plant must have the green chlorophyll pigment to make that sugar from sunlight, water and carbon dioxide. When it makes sugar it also needs minerals from the soil to make all the other compounds that are needed to sustain life and growth.
A plant with some green chlorophyll does not necessarily have to look very green - light greenish-yellow might be enough.
Milkweed (Asclepias) will sometimes produce white stems (my sister-in-law found one last year). The white plant grows and flowers seemingly on its own. Seemingly impossible to do. But when the plant is carefully dug from the soil a (sometimes long) connection is found to a nearby green milkweed plant.
It is possible to do simple tissue culture at home.
