If I understand correctly, and using Northwind as a (hopefully similar
example), how about the below; note that it only does a single SQL
query (because we force the ToArray()), but to be honest, I wouldn't
shy away from 2 simpler selects - one for just the total Count(), and
one for the Count() with a Where()... anyway, see how this goes:

               var data = ctx.Customers.GroupBy(
                       cust => cust.CustomerCustomerDemos.Any() ||
cust.Orders.Any())
                       .Select(grp => new { Linked = grp.Key, Count =
grp.Count() }).ToArray();

               foreach (var row in data)
               {
                   Console.WriteLine("{0}: {1}", row.Linked,
row.Count);
               }
               Console.WriteLine("Total: {0}",
data.Sum(row=>row.Count));

There might be some other options... I'll see if anything occurs...

Marc

I found a better answer; the tricky part was getting
deferred execution, as normally Count() executes immediately.
(of course, you could just do 2 simple queries? one Count(),
one Where().Count())

I've approached this instead by using a projection from the
primary table, and used FirstOrDefault, which means that
even if there are no rows, an object with 0 in both counts
is returned.

Aside: note that the .Count(predicate) [even with the Expression
form] does a very funky looking query, hence the simpler
.Where(predicate).Count() usage.

Anyway, the C# is:

var counts = ctx.Customers.Select(x =>
   new
   {
       Total = ctx.Customers.Count(),
       Linked = ctx.Customers.Where(
           cust => cust.CustomerCustomerDemos.Any()
           || cust.Orders.Any()).Count()
   }).FirstOrDefault();

With the faitly reasonable-looking generated SQL:

SELECT TOP (1) [t5].[value] AS [Total], [t5].[value2] AS [Linked]
FROM (
   SELECT (
       SELECT COUNT(*)
       FROM [dbo].[Customers] AS [t1]
       ) AS [value], (
       SELECT COUNT(*)
       FROM [dbo].[Customers] AS [t2]
       WHERE (EXISTS(
           SELECT NULL AS [EMPTY]
           FROM [dbo].[CustomerCustomerDemo] AS [t3]
           WHERE [t3].[CustomerID] = [t2].[CustomerID]
           )) OR (EXISTS(
           SELECT NULL AS [EMPTY]
           FROM [dbo].[Orders] AS [t4]
           WHERE [t4].[CustomerID] = [t2].[CustomerID]
           ))
       ) AS [value2]
   FROM [dbo].[Customers] AS [t0]
   ) AS [t5]

I have looked at the query plan/IO, and it isn't doing anything /too/ crazy.