How many include an RRC?

No, there is not a way to check status other than the IRS website.  Please don't waste IRS time by calling and asking them to use the same source.  The IRS tomorrow will probably update how many returns they have in the processing pipeline, at

https://www.irs.gov/newsroom/irs-operations-during-covid-19-mission-critical-functions-continue

The last count was 18.1 million.