Can I use a Savable Data Page with an Activity-based Save Plan that enqueues the save to be performed via background processing?

Yes, although the data on the Data Page will need to be enqueued using "Queue current snapshot of page" when using Queue-For-Processing (or Queue-For-Agent if you are still using Agents), as the Data Page itself is not a concrete instance that can be looked up by ID when the Queue Processor. 

It may be necessary to clone the Data Page to a separate top-level page to become the step page of the Queue-For-Processing step, so as to prevent the Queue Processor from referencing the Data Page in its separate Requestor which may cause it to reload the pre-saved state from the Data Source.

Discussion on this topic was sought from the LSA Data Excellence (Pega 8.4) webinar conducted in July 2020. The webinar and its full set of discussions that arose from it are available at LSA Data Excellence: Webinar, Questions & Answers.