Not what I would recommend. You would have to make sure to install apps, updates/patches, and settings on both. Not efficient at all.
If you want optimal speed and want more space, then raid 0 is your answer, but if one drive goes bad then you have to re-install everything. Raid 1 provides some protection as they mirror each other - if one drive goes bad, replace it and the array will rebuild your data automatically.
Other raids beyond 0 and 1 require more drives.
But the real answer is to make a backup image of your 'pristine' installation - OS, apps, utilities, settings - onto removable media that can be protected (a fire safe or relative/friend's house). The only problem with this approach is you restore back to that point - so if you only do backups once every year or so.... that's a lot of lost updates, patches, and data.
For your purposes, I suggest going with raid 1 since you seem to want to be able to quickly be back up and running.