Synthetic CDO - Prob overthinking this but wanted to check

I understand the idea that cash CDOs need an interest rate swap to cover the floating payments to floating note holders, but are they needed in synthetic CDOs as well. Specifically, would you need and interest rate swap AND a credit default swap in a synthetic CDO?

If you need to manage any rate mismatches, then yes. In practice probably not since cash raised would be invested in floating assets vs the floating notes.