Not really for some. Take, in the origin material, Burai and Mikoto Nakadai for example. Both didn't redeem until much later until the end of the series when both found out they were pawn of the bad guy's game. They redeemed quickly after but for all those who were evil before, Redemption Equals Death. Ditto for Rio and Mele.
Some of the Villians in Every Power Rangers/Super Sentai series are grumpy tropers too. (For Example, Goldar (Griffizer) is one of the Grumpy Troper).
However, to press on the point, evil Rangers must be cleansed by death to be considered redeemed, Wolzard of Mahou Sentai Magiranger is a more optimistic example (the same having happened to his counterpart Koragg in Power Rangers Mystic Force), while Burai, Mikoto, Rio and Mele died at the end of the series (they come back as ghosts giving our heroes advice). Wolzard technically died at the hands of the Big Bad along with Hikaru, both got better in the end though.
A straighter example could be Eiji Takaoka, a.k.a. BoukenSilver, who started out as a Jerk Ass loner whose only motivation was to hunt and strike down the Ashu. It's not until the team gives him his Sagasniper (with a convenient excuse from Akashi) that he accepts to join the team and gradually warm up to them.
Life-action subversion: in the mostly idealistic universe of The West Wing, Toby Ziegler is a grumpy, prickly grouch who is nevertheless easily the most idealistic member of the President's senior staff (which is saying something, considering they're all pretty idealistic). Indeed, part of the reason that he's so grouchy is that he spends most of his time embroiling himself (oft-times unnecessarily) in shouting matches and heated disagreements with people who are a little more practical than himself.
Dorothy of The Golden Girls tends to be much grumpier than the rest of the cast.
Emerson Cod and Lily Charles from Pushing Daisies, whose cynicism seems rather odd in the vibrant Sugar Bowl they live in. Considering that Emerson had his heart broken and his daughter kidnapped (twice!) and Lily's heart-breaking experiences with Charles Charles (Vivian's fiance and the father of Charlotte "Chuck" Charles) I'd say that their cynicism is hardly unjustified.
Like his film counterpart, Grumpy Dwarf in Once Upon a Time is quite sour, a trait that extends to his Storybrooke life as the self-described "town drunk" Leroy. Of course, he wasn't always grumpy. He had to get his heart broken to end up like that.
Rear Admiral A.J. Chegwidden in JAG often displays such characteristics, even though he has more gentle sides and genuinely cares for his staff.
Artie from Warehouse 13. This is even Claudia's nickname for him.
for example: Rocky the Lebanese Rambo tends to get grumpy more than his cousins.
Bobo Gigliotti even fits in to this, even. In Freaky Pizza, Bobo was on the phone talking to the clown name Ronnie Mc Doggle, who was also really grumpy, all because he has been waiting for his pizza for over an hour and his pizza gets cold.