And would adding more miners (supply) increase or decrease the transaction time? 
Yes. If you have more miners, or rather hashrate, then the rate of the blocks being mined increases, until the difficulty readjusts. The network attempts to keep the block intervals at 10 minutes. It would have the most impact if the hashrate is suddenly increased right after the difficulty adjustment.The main crux of the issue lies with the capacity of Bitcoin. Each block is limited in size and a block is usually mined at an average of 10 minutes. This means that for every block, there can only be so many transactions being included and confirmed. Having a long wait before a confirmation is usually a result of the lower fees being paid.
