>will it sync smart previews of all of my 250,000 photos or only the collections i tell it to sync?
Only the ones you tell it to Sync
>will it essentially back up a copy of my lrcat file itself?
No definitely not.
>i back up my library file with dropbox, but i'm wondering if this is redundant if i'm syncing.
No backup is not redundant at all. One problem is that if you kill your current catalog and don't have a backup you can't sync another catalog with what's on the cloud. It has to be the same catalog (or a backup of it). If you sync with another catalog, it will wipe out all the data on the cloud part.
>also curious if i can use the syncing feature to work on the master library across computers, like if i'm editing on my iMac and then switch to my laptop and back again.
No it can't do this for the reasons mentioned above. Only way to do this is to put the catalog on a portable hard disk. Some people put it in their dropbox folder and put the images on a NAS and have the catalog file sync that way but this is really dangerous and can lead to corruption of the catalog file if you're not super careful. The catalog file also can't be on a network drive so the only realistic option is to put it on an external disk. You have really large SSD based USB sticks nowadays that might actually make it realistic to just use a stick for your catalog and a subset of your images.
You can only synchronize specific collections that you create. You should not consider synchronized collections as a backup of your catalog. That is the purpose for synchronizing.
You cannot synchronize a catalog across computers. The catalog must be on a hard drive that is local to the computer running Lightroom. The easiest way to work on images on computers is to have the images and the catalog on an external hard drive that can be moved from one computer to the other.