Can cephalexin be used to treat an abcess?

Yes but you need a full course of them, not left over ones from another infection. You shouldn't have any at home. You're supposed to take them.

The very short answer is "Yes"
Yes, Keflex (cephalexin) is commonly prescribed to take care of abscesses and the bacterial infection that causes them.
I was just prescribed this a month ago for a possible bacterial infection at the site of an iv.
Four important things-
1)If you are allergic to penicillin, you may very well be allergic to this Rx
2)The pain of an absessed tooth is excruciating and at times after taking the medication for a short while, it may stop hurting but you really need to follow through the full course or you could build up a resistance
3)After taking Keflex for the absess you will need some sort of dental work done or the infection will return and could damage your heart. Usually a root canal is done and in extreme cases, the tooth is removed.
4) good bacteria can also be killed with the bad. Often lactobacillus and acidophilus containing foods or supplements can help this from happening.

That might be more of an answer than you were hoping for but I'd feel irresponsible not including the other information.

I'm not a doctor or a dentist though, so take what you will from it.
Hoping you have good health and pain free days ahead.