You will struggle somehow in the early beginning but after while, you may be able to understand the differences.
The differences between both dialects may be, but not limited to:
1) The pronunciation of some sounds for instance ق and ث, there are no such letters in English language, but the first one is close enough to K and the second one close to (th or t). I can tell that you can familiarize yourself with this distinction.
2) Use of completely different words for the same meaning such as : الحين in UAE, in Levant: هلا different words mean now.
2) some words exist in one dialect while don't exist in other. This one you should learn because even me as Jordanian may don't know. In my opinion, those words are countable and can be studied separately.
In general, whether dialect you intend to learn I think Arabs can understand you, but it would be hard for you to understand.