I don't think the F-16's are absolutely necessary; but would be very helpful, on offense.
I say not necessary as their air defenses are still awesome. Russian pilots are afraid to venture into Ukrainian air space so they shoot from Russian territory. So I don't think they are critical as a defense.
What is more critical, today, is HIMARS and rockets that have further range than the 40-mile ones being supplied to them today. They have 12 HIMARS. Give them 150 HIMARS and the Russians are retreating back to their 2014 lines, or all the way back into Russia.
The F-16's would certainly help that, but I think the HIMARS and longer range missiles (I think we have up to 200 mile range missiles for the HIMARS?) are more critical.
Where I think the F-16's are more critical, is an attempt to retake Crimea. Which is an extremely difficult task for Ukraine, a near impossibility without a Navy to speak of (especially in comparison to Russia) and a thin isthmus as an entry point into the virtual island. To invade Crimea, they'll need massive troop transports either by sea or air, and an F-16 force that can control the skies and cover for the invasion.
The Ukrainians are worlds away from attempting to retake Crimea.
But they could certainly push all of the Russians back into Russia from the Donbas and other eastern parts of Ukraine (sans Crimea).