Do most Greek speakers articulate the distinction between single (άμα, αλά) and double consonants (γράμμα, άλλα) in careful, enunciated speech?

No. Gemination is preserved, but only in the South-Eastern group of dialects (the most prominent member of which is Cypriot). And the gemination of those dialects does not always coincide with the orthographic gemination preserved from Ancient Greek. In all other dialects, and in Standard Greek, double consonants are for spelling only. (Just like in Modern English.)