Question: I've never played Pandemic, but thinking of getting the Legacy edition. Is it possible to play it without the legacy elements a few times first, and get an experience that is same or similar to that of the regular Pandemic?

Answer: 
Yes, you could play something very similar to vanilla Pandemic using just the base game components and ignoring all the Legacy elements. The board is slightly different, but you probably won't even notice.

You can really only do this before you start playing the legacy version though. Once you start playing the legacy version, things will happen that will modify the game in ways that will quickly make it difficult or impossible to play the base game.
Like people said before, it is easy to play vanilla pandemic with the pandemic legacy box. Moreover, various extra components/rules supplied with the game and gradually revealed through the game make it possible to play many interesting modifications of the game even after you finish the campaign.