Would this reduce transaction time?
The minimum average confirmation time is 10 minutes regardless of the total hash rate. That is how Bitcoin is designed.
The average confirmation time is affected primarily by the amount of the fee paid by the transaction and its size (in bytes), however it cannot be less than the minimum average confirmation time. Again, it is not affected by the total hash rate.
Finally, every user mining on their PC will not have a detectable affect on the total hash rate. A top-of-the-line PC might have a hash rate of 1 GH/s. If 1 million users mine on their top-of-the-line 1 GH/s PCs, they will contribute 1000000 GH/s, which is about 0.02% of the 5635000000 GH/s total hash rate.