I am developing a SF AppExchange application that works with Group Edition licenses. It seems that access to the API is allowed in Group Edition orgs as part of a managed package, so our application seems to be working well with GE/PE. However, there doesn't seem to be any clear documentation from SF as to how many calls there are available to the API for GE/PE orgs using a managed package. Anyone have any ideas?
From my experience, the limits are the same as Professional Edition. You have five full users worth of API calls. These API calls are limited to your package, meaning your clients can't use the API even though you can. You get 5,000 calls per day, the minimum for any non-Developer Edition that has any API access at all.