Can my cap-exempt employer apply for H1B during my F-1 OPT grace period, after my OPT has expired

I am on F-1 OPT. My employer is in the process of applying for an H1B for me, my employer is a university and is cap exempt. Can my employer apply for H1B after my OPT expires, but before the end of 60 day grace period of OPT? Is it legally possible, what are the risks? My employer could also provide an explanation for the delay in applying for H1B.