It would depend on what your change management policy is? Who is changing your environment? Are they always changing the active box? If someone is testing out new monitors on a standby box and just wanting to evaluate how they do over a period of then and you sync over it, they won't be happy.
What happens if someone added a VLAN to a box and didn't add it to all of the boxes, now your config sync will fail. Sames goes for a new floating self IP without a non floating on that VLAN. I think it'd be more useful to generate a "notification" of changes on each box, a diff of the configs and say do you approve these changes. Click yes, then it syncs the config.
At that point you'll have spent a week writing a script to save 10 minutes of config sync work which should be covered in any changes that are made (IE if you change a VIP, you test it, why would you not sync the config?).
TLDR: I don't think it's worth the time it'd take and there are a lot more necessary devops scripts or documentation work that'd be more helpful.