The short answer is NO.
Unless you are sponsored by a company that is going to employ you BEFORE you get here, is willing to do all the paper work, justify why they are hiring a foreigner instead of a local national, deal with all the bureaucracy to get you a Type D visa and then get you registered with immigration authorities (OVIR) it isn't going to happen. And most Ukrainian companies WON'T do that. Only foreign companies already here that need you will. The best you can do is come here visa free for 90 days and teach some English at a Mom and Pop school and then be out of Ukraine before your 90th DAY expires.
Sorry to burst your bubble but the truth is less painful than the scams run here to clean out your wallet that say they can get you to stay. I have two letters for those scams...BS.
I have been living here for six years and married to a Ukrainian National. My best friend here is a Ukrainian Lawyer. I know of what I speak.
Best wishes, Steve