I think Liverpool have already demonstrated a lack of sense re: how they have handled the entire thing to be honest (irrespective of whether they appeal). They, quite correctly, came out and condemned Suarez's actions very quickly, and dealt with things from their end swiftly and strongly, but made a complete balls up by then challenging the FA's assertion that 3 match ban would not suffice.
To any objective and reasonable person with any understanding of the disciplinary process, it's always been perfectly obvious that biting another player in the manner which he did (yes, that's right, MANNER, for those desperately, and erroneously, comparing this to the Defoe incident) was worthy of greater punishment than the standard penalty.
One suspects, that had they taken the punishment on the chin and accepted responsibility, or at the very least had the sense to wait and see what the FA's punishment would be before releasing statements that were always going to antagonise the powers that be, he would have copped a lesser penalty. Instead, they basically waved a red rag to a bull, and are now crying about the consequences. This will only be exacerbated if they appeal, but since he's their most valuable player and they can scarcely get by without him, they may feel they have no other choice.
Hopefully we'll see some more hilariously dire "Save Luis" shirts this weekend.