The difference here in whether a RAID 1 controller can accelerate the disk reads in the same manner as a RAID 0 controller is whether the RAID 1 controller has enough on-board cache to perform the block reassembly.
First, let's be clear that you cannot think about what a RAID controller is doing in terms of files. The controller knows nothing about files and file systems, it only knows about blocks.
If the computer wants to do a 25MB read from the controller (50,000 blocks), the controller receives a request similar to: "I need blocks 100,000 through 150,000 from the disk". Let's see how a RAID controller could answer this request in each case.
Let's assume we have a 2-drive RAID 0 with a stripe size of 32K. That means that every 16K (32 blocks) is stored on the other disk. i.e. Blocks 100,001 through 100,032 are on disk 0, blocks 100,033 through 100,064 are on disk 1, and so on.
To answer the computer's read request, the controller will begin sequentially reading blocks on both drives. As it gets each group of 32 blocks from drive 0 and the 32 following blocks from drive 1, it assembles them together into 64 blocks in the correct order and sends them to the computer. The computer believes it is getting blocks from a single disk, in order, and is none the wiser. The RAID controller needs at maximum a chunk of memory equal to the stripe size (32K) to perform the block reassembly.
Now let's look at a 2-drive RAID 1. In this case, all blocks are duplicated on both drives. Blocks 100,000 through 150,000 exist on both drives. Like russki said, you do not want the actuator arm jumping around on each drive because that will destroy any read time advantage. Thus blocks must be read sequentially if you're to have any hope of improving the read speed.
What you can theoretically do is take the 50,000 block read request and divide it in 2. Have drive 0 seek to and read blocks 100,000 through 125,000, and have drive 1 seek to and read blocks 125,001 through 150,000.
The problem is that the computer must receive the blocks in order. Thus, you must buffer drive 1's read data in the RAID controller's cache, waiting for both drives to complete the 25,000 block reads. Once drive 0's read is finished and you send blocks 100,000 through 125,000 to the computer, you can now send blocks 125,001 through 150,000 to the computer from cache, which is much faster.
However, in this case, the RAID controller needs 12.5 MB of on-board cache to perform this trickery.
Thus, a typical motherboard RAID 1 implementation (like the NVidia or Intel south bridges) cannot perform accelerated reads in RAID 1 due to the lack of cache. But high-end RAID cards with on-board cache can and do use parallel reads in RAID 1 to achieve faster read speeds. The LSI MegaRAID controllers (who make many of Dell's PERC series of RAID controllers) can do this.