Does the Use of AuxPoW Slow down the Block Production of the Primary Chain?

No, the use of Auxiliary Proof-of-Work (AuxPoW) does not slow down the block production of the primary chain. The process of merged mining simply involves including an extra piece of data (the secondary chain's block header) within the primary chain's block.

The primary chain's difficulty target and block time remain governed solely by its own hashrate and difficulty adjustment mechanism. The extra data is negligible in terms of computational effort required to find the valid hash.