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You're right - most plants are green, but for the rare ones that are not, chlorophyll is kinda like an enzyme: it speeds up photosynthesis. So it will photosynthesize, but it would be less efficient than green plants.
chlorophyll is the green pigment which is in plant leaves,there are different kinds of chlorophylls,green one is the most active one,yellow color is called as xanthophyll,orange colors are carotene, bright red and purple colors are anthocyanin.plants which have colored leaves do perform photosynthesis but not efficiently as green chlorophyll.
plants with non green leaves also have chlorophyll on their leaves but the quantity is comparably less to other pigments which masks the green colour.