If the given exchange does not require the KYC procedure to go through out, why not. Even some dedicated mixers use coins acquired on exchanges to provide them to their customers, Look, for instance, what MixTum says:

 

 
Choosing this approach do not use address generated by   SPV wallet that was previously connected to 3^rd party server as more likely than not they already know it.  To preserve your privacy run your own node, For instance, when mixing my coins via exchange I'm using the following bond  Passport2(hardware wallet) - Sparrow(light client) - Bitcoin Core(node). Passport2 secures receiving addresses, Sparrow insures good control of all relevant stuff (addresses, UTXOs, transactions, fee, etc) while Bitcoin Core  broadcasts/receives transactions.