Firstly, repent, for the Kingdom of God is at hand … you knew that was coming.
Secondly, preachers that tell people the Christian life is the happier life should be defrocked. Or worse. Firstly, they debase what our faith is all about – it's not about us – and secondly they have completely misrepresented the entirety of Bible's description of "the life" in Christ – we're not enduring persecution even to death because it makes us happy, that's insane. This "Christianity makes me happier" kind of theology is errant bullshit, pardon my french, and should be excoriated from every pulpit worldwide. It is worldly, it is sending the wrong message, and it is not preparing the people in the pews for the true nature of the life path they have chosen.
So, in short, OP, no, if your happiness in this life is what is most important to you, then being a Christian will totally derail that.
Now, this does not mean we live lives of abject misery: there is joy. We laugh as our Lord laughed, as indeed any man does; we find joy in the things of life, we mourn, we cry, we are morose, we find satisfaction … just as the world does, just as our Lord did.
But, yes, the path of a Christian IS one of self-denial, of reforging our behaviours and thinking, our desires and our wants, to align with the truth of who God is. We're not legalists with our flesh because it makes us happier, we do it because we are in a loving relationship with a God who is different, higher, purer, more moral, more compassionate, more loving, more merciful than the world is, than we are, and we want to live lives that imitate Him. We, like a bride wants to look pleasing for her husband, want to be pleasing to our God. It's in our new nature to want to reflect the values He reflects, to love the things that He loves, to BE what He is. The things we deny ourselves are still appealing to us, but at a kind of bodily way. This is why some Christians still fall into sins, have sex they know they shouldn't. The difference is that they know they don't want to do that anymore.
And that's where the real pain, the unseen pain of being a Christian, kicks in. We struggle with this tension between the carnal self, what St Paul calls the Flesh, and the renewed mind. Our conscience is constantly at war with the old self, and this produces a poverty of happiness, made worse if we linger over the band-aid, slowly peeling it off rather than wrenching our old ways from ourselves. This is no small thing, but it is both a desirous and necessary thing, to be more like our God. And we want it more than what the world can offer because we know that all that the world can offer, the sins of the flesh, are transient … fleeting … not permanent, nor representative of the lives we will ultimately live. YES, it is true that we know that the TRUE reward for this life lived in service is beyond this world. We have a HOPE in the God we serve that transcends this life. Jesus promised that at some time, our bodies will be exchanged for pure bodies that no longer lust after things not aligned with God. Then our purification, and joy, will be made complete.
What I'm trying to do is dispel this notion that we live in futile self-denial grumpily declining to satisfy our "normal desires" for some ethereal hope. Adam4d has a great cartoon on repentance wherein he shows what bad repentance is, where the person really doesn't want to change but forces themselves to because "rules". It isn't about "rules", it is about wanting to be what God planned for us, about being in alignment with the One who redeemed us. And we WANT to be transformed. We HATE our old selves. We earnestly TRAVAIL to be without sin. And "travail" is the right word: it is hard, painful, often joyless, and tiring. But also necessary, desirable, and fruitful.
But, to answer your question, would you be happier … short-term, maybe not; medium-term, yes, I think you would; and long-term, peering beyond death, most definitely. But, for this life, on balance, probably not. For as St Paul wrote: ((( if the resurrection never happened, then we Christians, above all others, ought to be pitied most among all men. )))