Sorry to quibble, but if you're on income support then you're not getting Incapacity Benefit (which is contributory only). If you get moved onto ESA it will be Income Based, which isn't time limited. So your main worry is whether you get found fit for work, in which case your income support will reduce to same rate as JSA (which is also the rate you get if you appeal and are waiting for it to be heard).
People do get IB plus IS
Yes, if the only family income is Incapacity Benefit (i.e. there are other dependants e.g. children), then it will be topped up with income support. However, if the Incapacity Benefit stopped, the income support wouldn't, and would be topped up to the level required. This would apply whether the previous income was Incapacity Benefit, but was now JSA. The end result would be the same level of income support in both cases. The IS level of minimum need requirements for a family to live on doesn't change just because an income reduces.