Has anyone run a regular campaign of Capes, and occasionally had people who wanted to participate for a single session? This seems very easy to do, but I'm wondering if there would be negative consequences to it. I mean, the obvious potential problem is major disruption to the story, but I'm also thinking it could possibly mess up the currency system.

The issue I would see is that in a long running game, the players would build up a good understanding of what each other player likes, expects, and rewards.  The new player would throw that calculus off a bit.

As Fred (Vaxalon) said, the "vibe" of mutual understanding among people who've played together a while is the big issue -- but whether it's a problem or a source of excitement depends entirely on the people involved. Some bands can do great things with a new guitarist coming in for one concert, some get thrown off. I'd be leery to bring a "guest star" into the ongoing campaign I'm in, for example, but it's a time-travel soap opera which has developed a huge density of entangled plot; a more standard superhero team-up/smack-down campaign might really benefit from regular guest players to do special villains or "crossovers."

The reward economics seem pretty robust, honestly. Our campaign hasn't had "guest star" players, but we did lose a regular player altogether after the first few months, and while she took all her Story Tokens, Inspirations, and Debt-laden spotlight characters with her, the game economy didn't collapse or even stumble particularly.