If they enter open confrontation with Russia, they can kiss their chances of EU integration good bye. The last thing EU needs now is to take side of a country in an open war conflict against Russia.
If they stay clear of a military conflict, but try to get into the EU, Russia will just hike gas prices, tax or close their imports and Ukraine will be a deepest financial butt of its entire existence. Again, would EU be even slightly interested in getting Ukraine on board? Rhetorical question.
Ukraine is a strategic buffer between Russia and EU. Russia won't let Ukraine go. Period. Therefore, Ukraine has exactly two options - stick with Russia or split into Western (Ukrainian) and Easter (Russian) parts. But then, if they split, then most of the industry and resources is in the East, so Western Ukraine will again come out free, liberated and utterly broke. Its chances of getting into EU? Slim to none. Whichever way you slice it, they just can't get into EU.