In this situation, the phrase "as happy as" functions in a similar way to "Even though..." With this format, there is usually a 2nd part that is compared to the 1st part. For example: "As happy as it would make me to fly to Paris, I still cannot justify the expense." "Even though it would make me happy to fly to Paris, I still cannot justify the expense." You can use this with other feelings as well: "As hungry as I am, I refuse to eat at that restaurant." "Even though I am very hungry, I refuse to eat at that restaurant." Good luck!

The first is a dependent clause, not a sentence. The second is a sentence that makes no sense. It is not possible to say what "as happy as" means in the sentence because the sentence says nothing.