Is it a good idea to send my resume out early?

I’m graduating college in June with a BA in Chemistry and a minor in Criminology. I’ve made a resume that I think is pretty solid, and I’ve been looking thru jobs that I’d be eligible for with my degree. What I want to know is if it’s a dumb idea to send out my resume to potential employers now, even though I don’t have the required degree for the jobs? Like, would they be willing to interview me and such, and then hire me on after I graduate? Or should I just wait? If it helps any, virtually every job I’m looking at would be doing labwork of some kind (some examples were the chemist at a free clinic, a CSI, research projects for various companies, crap work at a hospital, etc etc). Thanks for your help!