They're still nowhere near the league of Ukraine's upgraded MiG-29 and Su-27 though and would be a notable downgrade. Sending them inferior planes would probably be a bad idea as they can't afford to be wasting pilots.F4-E's are still an awesome kit of fighter, Japan, Greece, Turkey S.Korea still use them.
The idea that it would be quicker to train up on an F-4 than an F-16 is also debatable as older planes can in many cases be more complicated/difficult to operate. I would wager that an accomplished fighter pilot would master the F-16 quicker than the F4.