If you took a questionnaire online with the idea that when you finish you will get training, and after you finish the questionnaire you are presented with a popup box asking you to "Like" the questionnaire page on Facebook before you get your training, would you press "Like"?
I wouldn't click "Like" because clicking like signs you up for spam:
Facebook sometimes makes very curious decisions with respect to user privacy. Recently, one of them came to my attention, and it is so comprehensively wrong that I had to put up a public service announcement about it.
You've seen the Facebook "Like" buttons all over the Internet, right? Liking anything lets the owner spam you. No, really. If you doubt me, click the Like button on this page: you'll find a message from me on your News feed (the big list where you see updates from your friends) within 5 minutes, unless Facebook has shut down this tech demo since publication.
The only way to get a valid answer is to test it, count the number of users who get that popup and the number of users that click like and continue to the training - now you have the exact percent of your users from your specific audience that don't want to like you and you can make the decision how many users you are willing to lose to be liked on facebook.
And I wouldn't click like because I don't have a facebook account! (I know, facebook has more users than there are atoms in the universe but people like me exists and if you want me to use your site (or buy from you) you have to respect that).
I wouldn't press "Like" either - not before seeing what kind of training I would be getting. When you Like something on Facebook, it's a sort of endorsement - an advertisement to your friends and I wouldn't endorse something unless I find it worth while. Also, I personally am very wary when a webpage tries to make you Like something before you see the content.
I would suggest you let your users browse the training pages, and popup your question after a certain amount of time. If you give your users great content, they'll be more inclined to "Like" your page without you having to force them to do it right off the bat.