Lets say you have two hard drives, A and B. You are transferring a very large file from hard driver B to and external Hard drive C. Would that make the hard drive A lag? Hard drive A is the main drive by the way and it holds the OS and everything. Hard drive B is just a storage drive.
I don't believe HDD A would lag if it is SATA as each SATA connection acts as a dedicated connection for each drive. However copying a very large file would require CPU and RAM resources that would certainly impact on a low spec PC and to a lesser degree a high spec PC.
As long as everything is set up correctly the I/O between drives B and C shouldn't have any effect on drive A. But if you've got some configuration issues there can be an impact. For example, if the drives are running in PIO mode then the one transfer will probably use up all your available CPU time and not leave anything left over for other work.
No noticeable lag.
Sata is a point to point architecture. When B is transferring data on the bus, there might be some minimal interference. But the maximum hard drive data transfer rates are half the capability of sata2. If your external drive is usb, it can recieve data at a much lower rate, minimizing the interference even more.
Lastly, the OS on drive A does mostly small random reads and writes which take up little of the bandwidth.