Not really. But there are a couple of ways to mitigate issues.
Each monthly update will be the previous month's update plus the new updates for this month. Strictly the only way to avoid a particular update is not to apply that or future updates. Obviously (in the case of security updates at least) that would be stupid, so what can we do?
There are actually THREE different updates provided each month.
There is a "Security and Quality" update released on the second Tuesday of each month (aka "Patch Tuesday"). This contains the security updates for that month and the non-security critical and routine updates for that month. as well as all previous security and updates This is the recommended update (Microsoft recommended, and given the poor choice of options, begrudgingly the most sensible update track)
There is a "Security ONLY" update also released on "Patch Tuesday" This contains ONLY the security patches for that and previous months and could be applied if you have a need to avoid a particular month's "Security and Quality" update.
If you need to fall back to the Security Only update for a particular month, I suppose that you have to hope that MS will fix any issues within a month or at most two (I know - I wouldn't hold my breath!), allowing you to jump back on the "Security and Quality" track. So the first mitigation is to temporarily fall back to security-only updates.
Oh yes,..... I said THREE updates.....
On the Third Tuesday of each month MS will release a "Preview" update containing the non-security updates planned for the following month's patch Tuesday. This can be used on test servers to check for issues related to the non-security content planned each month (and give you more time to recognise those issues). The second mitigation is to pre-test the non-security updates if you have the means. (We all have the time, of course! - err thanks MS).
So all's OK then.... . Now we've cleared that up ... there are a couple more things worth understanding about the new scheme.
In WSUS all of these updates are under the Windows Server category, the first two categorised as "Security" and the preview classified as "Updates", so you can sort of mange them in that way. I tend not to approve the security-only update unless I need (in order to avoid confusing installations depending on installation order)
There are separate groups of updates for Windows and .NET, so you will likely get one of each of those patches each month.
And now for a big gotcha.... In a prominent blog post, an MS technician says that you should enable "Express updates" in WSUS..... What he does not point out is that doing so will cause massive downloads of additional WSUS content. You may well find that your WSUS cache increses in size a few times over (possibly up to 1TB for a typical selection of MS products and versions). Additionally, once you tick that box, there is no doing back - you cannot untick the box and go back to where you were (at leat not without entirely rebuilding your WSUS cache from scratch and performing open heart surgery on the WSUS database). I suspect as the cumulative updates grow in size, the Express updates will become more of a necessity and less of an option. Also note that SCCM does not yet support express updates... Of course we all have oodles of disk space just waiting to be allocated to our WSUS cache and plenty of Internet bandwith to download the updates so again no problem....
And finally, it's worth noting that MS are initially basing the cumulative updates starting at last month. For the next few months (until January 2017) all of the cumulative updates will be Cumulative from October 2016. From February 2017, MS will start rolling in earlier updates, aiming to complete the task over several months. At the end of that period all earlier updates will have been subsumed.
Good luck (we will all need it!)