That depends on whether or not they pack The Numbers Game. If they forgo Numbers Game, they may pack Cavalry. If they pack Numbers Game, they are a Stable, and cannot pack Cavalry.
Does Numbers Game matter? Since they only become stable once Numbers Game is revealed and not during deck construction as Numbers Game doesn't have the "when packing this card, you are a stable" text. The sentence that declare you are a stable is on a different sentence and line, so it doesn't take effect until the game started.
The Numbers Game
Backstage Card
Can only be packed by Right To Censor, Hall & Nash, The People's Team, The Dangerous Alliance, FBI, The Home Team, The Heat Seekers, The Spirit Squad, or a Stable. When packing this card, you may pack Handicap Match.
You are a Stable, and your opponent cannot play Handicap Match. When he is not a Stable, you may ignore the "Can only be played..." text on Handicap Match, and he must discard 1 card to play a Run-in.