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Not exactly if you level up it it won't be too strong...
To be a worthy opponent you will need to inscrease it's speed and some strong TM( Especially Psychich) but if you evovle it it's another story...
Hope i helped...
It depends, really. Can you train it right? See, Clerfairy's highest base stat is HP, at a min of 70. Clefairy has a low base stat of speed. I would train my Clefairy by raising the Speed a little, but more of HP and Sp. Def with EV's, to further max it out. You'll also want to evolve your Clefairy with a moonstone, Clefable has an even higher HP base stat. Now, if you don't care about EV's and stuff and you just want to know a straight up answer to your question, In my opinion, I'd say a Clefairy is worth training. Of course, it's all in the eyes of the trainer :D Here is a Ref link
EDIT: To answer your second question, no, clefairy won't be weak if you spend time training it. You'll have to train it longer to get the preferred stats if you don't evolve it right away, but it still isn't weak.
I know the other peeps gave you advice. But, I must say, if you want a good Normal Type, get a Kangaskhan. If you're not that far in the game, I would suggest Jigglypuff. I just think it's cuter and has a better moveset.