A/B testing is fine and all, but you might want to think of it from an ethical standpoint.

Are you okay with requiring someone to shout "I like this service" to be able to use said service, on first use? Does it feel right to disclose the like requirement after the user has already put time in using the service?

It sounds backwards to me at least and you're definitely alienating some people, but if you think it's no big deal then you're entitled to your own opinion.

Rather than A/B test the conversion rates of liking before-or-after, think really hard about what you want to convey. What does a like give you? Is it worth alienating potential users?

You don't need an A/B test to tell you that "If you enjoyed our service, please Like us on Facebook." is a friendlier, more positive request. People have already tweeted about it more than they liked it on Facebook without additional prodding. Let the site stand on its own merits, rather than trying to force promotion through potentially sleazy methods.