Photo editing is fine as long as you’re not working with really huge files (hundreds of MB’s, as that may take a few seconds for the data transfer.
For video editing, it will largely depend on:
What bandwidth/data rate of the video (remember that bandwidth/data rate is independent - you can have 2 Mbps 1080i and 160 Mbps 1080i, for example)
Will you be editing multiple streams simultaneously?
Remember that Drobo doesn’t necessarily make disk speeds faster, it just makes the data safer (fault tolerant).
I do not recommend doing that…
Your internal HDD will almost always be faster than Drobo, unless you have one of the enterprise-end iSCSI Drobos, but then I’m not sure you’d be able to boot from iSCSI anyway.
If you have some kind of catastrophic error with your Drobo chassis or configuration that prevents you from accessing the Drobo’s files, you will have tremendously fewer recovery options than if you just had your data on a “regular” drive. Most data recovery places do not have the knowledge or hardware to be able to read a Drobo disk pack.
For your video editing and OS-level disaster recovery, I would be more inclined to use Drobo as a backup target for some kind of automated backup rather than using it as the OS drive.
Also remember that fault tolerance is not a substitute for backup, nor is a single backup truly “safe.”
Regardless of what you use for primary/working storage, you should still have backups of anything that’s important.
Definitely browse around the Drobo knowledgebase and other Time Machine-related threads here (though you can probably safely ignore the ones related to Drobo FS issues) for hints and tips on making Time Machine work properly with Time Machine. Drobo’s Thin Provisioning can sometimes confuse things like Time Machine and whole-disk encryption as both assume there is “real” free storage behind what’s reported.