Waiting for reconsideration, overstay status?

[noisycat]

My husband was refused because UKBA claimed we didn't submit a relevant document. When I called them they said they did actually have it, so we've asked for reconsideration. The document definitely invalidates the grounds for refusal, so I'm reasonably hopeful.

I don't really want to lodge an appeal at the same time. It's not a huge amount of money but we are having cash flow problems this month. If we don't do that, and they don't get back to us within the ten days, does my husband become an overstayer or are we in any danger of being given a 'leave within this timeframe' ultimatum? What do they do if they have you down as officially refused but you don't have an appeal in the works, just a reconsideration request?