Does proguard work to obfuscate static string constants?
No, ProGuard doesn't encrypt strings constants (Proguard FAQ Link)
But there are some commercial products which will help you with that.I would recommend the Stringer Java Obfuscator because it has the check call context and integrity controls features which makes reverse engineering as hard as possible. IMHO Stringer is the best string encryptor for Java and Android on the market today.
Also see Allatori Java Obfuscator.
N.B. I'm CEO at Licel LLC. Developer of Stringer Java Obfuscator.
What ProGuard does (if configured correctly to do so) is in-line string constants. It wouldn't make much sense to obfuscate them, think of it, a string constant could be used for representing a message to the user, and what good would it do if it were obfuscated?