While I don't speak for anyone at SIAI, several possibilities spring to mind.

• Accepting bitcoins relatively early in the game would tend to raise the status of an organization like SIAI should it prove popular, but doesn't cost it much if it doesn't.
• If the value goes up the organization can profit financially by holding onto them.
• It may be the case that people will donate bitcoins more easily than equal value in dollars, for psychological reasons (e.g. lack of equivalent ugh fields).
• It may be that people who initially consider donating in bitcoins will change their minds and donate dollars instead.
• It could plausibly come about that processing power, and/or the time and energy of AI hackers, can be purchased more cheaply/easily for bitcoin than dollars.

Or is it just that giving people more different ways of donating increases the average amount that they will give, and then SIAI can just sell bitcoins for US dollars when they need money?

More likely to increase the total - probably at the expense of the average.

I think Bitcoin is quite unlikely to completely collapse in the next year because there are enough people with a vested interest in Bitcoin going up (namely Bitcoin miners/hoarders) that would start buying long before the value of a Bitcoin approached .1 USD.