My 7-year-old iMac died. I don't plan to replace it. It is backed up to Crashplan. Is it possible to restore my iPhoto library to the cloud, i.e. iCloud or Dropbox, so that I can access the photos as needed from my iPad or iPhone?

Probably not - but that certainly does not involve iPhoto for the Mac - you need to look at Crashplan support for you options

And iCloud is not a place to store photos so that is certainly not a possibility

If you restore your masters folder out of the iPhoto library you will have all of your original photos to do with what you please

LN