I think you should be able to, but it will depend on your implementation. I know pure software raid in linux can do this. For hardware and driver-level raid, it depends on your system, so you'd probably just need to google it for your particular hardware controller. In any case your performance would be limited by the slower of the two disks. This is one reason why matched HDD's are preferred.
That brings me to the second part of your question. RAID 0 is also referred to striping. Simply put, with RAID 0, your data is stored alternating between the disks. Part 1 of a file is on disk A, part 2 on disk B, part 3 on disk A, part 4 on disk B, etc... When you read the file, both disks can run at the same time, so you can get part 1 and 2 at the same time, part 3 and 4 at the same time... It theoretically doubles the speed of the slower disk. This, however doesn't account for real world factors like seek times and CPU/controller load issues. Restated, if one disk is faster than the other, the speed is limited by the slower disk. Additionally it will give you a capacity equal to twice the size of the smaller disk.
It should also be noted that the failure rate is effectively doubled. If one disk fails you lose all your data. HDD's do fail, and now a failure of either one will amount to data loss. RAID 0 has no redundancy.
I run RAID 0 on my system and it is much faster for loading large files where seek times aren't an issue. It's nice for gaming map loads and other sequential reads. I also have a robust networked backup strategy due to the higher failure rate. The increased failure rate should not be ignored.
Now my opinion: get matched disks.