Non-Shanghai permanent plates are, in general, not prohibited within S20. 沪C suburban ones and temporary plates from other provinces are however prohibited.
As the link provided by @lambshaanxy says, they are now not allowed on the specified elevated roads within the area circled by S20 during daytime (7h - 20h) on working days. S20 itself is not on the list. Using the surface roads is still allowed.
However, more restrictions are coming after the 2021 Labour Day Golden Week. Non-Shanghai plates will not be allowed on surface roads within the Inner Ring during peak times (7h - 10h, 16h - 19h) on working days.