Can I get an F Visa(I have Letter of Invitation) even if I have less than six months left on ARC?

I have been invited to be a visiting scholar(F Visa) from a university in Shanghai and I have the Letter of Invitation. I finish my current teaching contract in Seoul on Feb 29 and plan to fly to China on March 1st. My Alien Registration Card expires on April 1st. I heard that the 6 month ARC rule only applies for people wanting to get tourist visa..
Can I get the F Visa even if my Alien Registration Card will expire soon?