No, it's not important to check that the tags are correct before answering a question - because badges themselves aren't that important, IMO.
If you consistently answer well in a topic, you will eventually get a badge for that tag. Could you maybe get there a tiny bit earlier by checking for tags? Maybe. Or maybe the extra time taken to check the tags will let others get in their answers earlier, possibly costing you votes.
Why does it really matter? Isn't the point to get accurate answers for those asking the questions (and future researchers)? Badges are a bit of fun, not the main goal.
EDIT: Changed tags for question to include "badges" and "tags" to make sure I get those badges that bit sooner...
(Seriously, it's worth editing a question's tags for the sake of accurate classification - not to get you more badges.)