The answer to this question depends on the condition of your gutters and downspouts. If both are in good shape, a good roofing contractor should be able to work around them or carefully remove and reinstall them once your roof repairs are complete.
If you’re replacing an old roof, your gutters may need some attention as well. Your roofing contractor will talk to you about this during your initial consultation. They’ll give you all the information you need to make an informed decision about your gutters.