Yes. All plants carry out photosynthesis. They all contain chlorophyll which is key for photosynthesis. The coloured leaves contain other pigments in addition to chlorophyll. Normally plants are green because of the chlorophyll which absorbs blue and red light from sunlight and transmits green light. Plants with purplish or reddish leaves contain a pigment called anthocyanin while plants with yellow or orange leaves contain a pigment called carotinoid. Anthocyanins give red apples and grapes their colour while carotinoids give carrots their characteristic orange colour.
Can you think of plants with different coloured leaves besides green?