Will pcsx2 Screw my Motherboard or GPU bios?

Depends:

Compare your system's specifications to the recommended/required specifications for pcsx2.

Here is a link that I found by googling "pcsx2 requirements".

https://wiki.pcsx2.net/PCSX2

There are other similar links as well.

If your system does not meet the minimal requirements then performance is likely to suffer.

Should not do any damage per se - just will work very slow. Unplayable.
 
May or may not.

Download the pcsx2 installation instructions.

Overall would not expect the installation process to do such things. However, once you start clicking "I accept" or "I agree" boxes who knows what the installation process may do thereafter.

Could even be something legitimate but due to your current system configuration - may not be a good thing to have happen.

Hopefully nothing malicious per se but that again depends on the source of the download. Scan the installation file(s) first.

Likewise check the source's Forums and FAQs. Read what other users are asking about or complaining about.