Not significantly so. You only need to transfer 150 KiBytes/sec on an interface that can support 100 to 200 times that rate or more. Even without DMA enabled it isn't a significant burden on the CPU. And memory usage isn't an issue at all since you aren't storing all the data, just buffering a few bytes at the most.
If we were still running 6502's or Z80's then transferring the data throught the IDE cable might be an issue (for more than one reason...
), but it isn't a problem for the systems we use today.