Does mixin count increase the time required for confirmations? Does a transaction with a higher mixin count have to "sit and wait" for additional transactions to occur on the blockchain, in order to mix with them? What if in a given minute or period of minutes, there are no additional transactions, only the "mined block reward(s)?" Can a high mixin count transaction mix with block rewards?
The way ring signatures work is the mixing is done entirely by you, on your own computer, with no outside interaction at all. There are no third parties, and mining has no role in mixing.
So to answer your question higher mixin count does not increase the time required for confirmations. It does make the transaction larger (in bytes) so it will require a higher fee, and if blocks are filling up it may have to wait a bit longer to make it into a block.