The short answer: yes, but timing matters. The longer answer depends on what kind of colour treatment you're getting and the current condition of your hair.
Permanent colour and bleaching
Permanent colour — and especially bleaching or lightening — uses chemicals that weaken the hair. The same two-week rule that applies after a relaxer applies here: wait at least 2 weeks after permanent colour or bleaching before getting braids. Braiding chemically processed hair too soon risks breakage, particularly at the points where the braid puts tension on the hair.
If you've bleached to a very light shade, your hair may need longer than two weeks and additional deep conditioning before it's in a strong enough state for a braid install.
Semi-permanent and rinse colour
These are less damaging than permanent colour. If your hair is otherwise in good condition and your scalp isn't irritated, you can generally get braids closer to the colour treatment — within a week or so. Still, it's better to ask your stylist than assume.
The best approach
If you want both colour and braids, do the colour first, give the hair time to recover, then book the braid install. If you want colour in your braids, consider coloured extensions rather than colouring your natural hair — you get the effect without exposing your hair to more chemical stress.
Tell us at your consultation if you've recently had any chemical treatment. We'll assess the hair before starting.