Check IEnumerable Count
I think your approach is reasonable if you don't want (or can't) have the whole collection in memory. One minor change: if you don't need the count, just whether the collection was empty or not, use a simple bool:

bool any = false;

foreach(var e in expensiveObjects)
{
    any = true;

    //other processing
}

if (any)
{
    //do something
}