No. If you were more familiar with the situation, you would understand that EU is only being used as a token signal (not goal) of the direction the country should be heading in. What the protesters really want is for the current government to resign and not to sign a (undoubtedly corrupt) deal with Russia that would effectively infringe on Ukraine's economic and political sovereignty.
It is utterly dependent on Russian gas for its energy needs. Even if Yanukovich steps down, next leader will have the exact same problem - where to get gas to power the country and you can bet your last grivna that the price of gas will go ballistic if Ukraine is to do something, anything to jeopardize the security of Russian borders. For example, align themselves with the EU. They are in a check-mate :-|
The vast majority of trade Ukraine does is with Russia, so souring that relationship will spell economic doom for Ukraine. Unless the EU is willing to purchase more products from Ukraine than Russia while at the same time providing them with loans and cheap gas I don't see how a trade agreement with the EU is a good thing.
It's not like Yushchenko was able to get anything beneficial from the EU, why does anyone think Yatsenyuk, Klitschko or Tyahnybok will do any better (assuming any of them could even get elected splitting the vote in the west)?