Downloading the client on one PC while playing the game on another PC. Possible?

Hi, I play the game on PC but lately my computer is having a lot of issues. I have a second PC in the house that I'm downloading the game client to now, but it's going to take 2.5 hours and I was hoping I could continue playing Endwalker on my other machine (troubled as it is) while I wait for the client to download on PC2.

I'm afraid to try this because initially when I was getting logged into the launcher for the first time on PC2, my account got temporarily locked for suspicious activity. I don't want to trip the security alarm again (and possibly have a harder time regaining access to my account) so that's why I'm asking here if there's any way I can do this. Thanks.