Will your photos also be on Dropbox? If not, maybe generate smart previews.
Also , you need to think about how you define "corruption". It's unlikely that the lrcat file will be rendered unreadable, but what can easily happen is that you work on computer A, then open Lightroom on computer B before the sync up from A and down to B is completed. There will be a "conflicted copy" of the lrcat file on Dropbox, but the big pain will be that you may overlook that you've opened an earlier version of the catalogue and might re-do work or assume pictures have been edited. So you need to be sure the sync upwards is completed, and that the sync downwards is finished before you open the catalogue on the other machine. I found this such a pain I don't use Dropbox for the catalogue, but some people do it.