Can AVerMedia device support HDCP HDMI input?

No.  If you connect an HDMI signal that has HDCP protection (Copy protected Content), then AVerMedia will not display video. Some products may use HDCP when you don't realize it.
Only when you are using an ios device (iPhone/ Ipad), you can choose HDCP off in RECentral to allow the capture card to receive video feed,



Regarding some TV box or apps, however, they may use HDCP when you don't realize even though you choose HDCP off in RECentral.  For example,  iTunes, Netflix, Huhu . That's how it's designed, HDCP is copyright protection.