Can you GROUP BY a CASE statement in SQL 2005?

Yes, you can:

create table x (col1 int, col2 int)
GO

insert into x select 1, 1
insert into x select 2, 1
insert into x select 3, 1
insert into x select 4, 1
insert into x select 5, 1
GO

select 
     count(*) as count
    ,(case 
        when col1 % 2 = 0 then 'Even' 
        else 'Odd' end) as what
from x
group by  (case 
        when col1 % 2 = 0 then 'Even' 
        else 'Odd' end)
GO

drop table x 

/*

output

count       what
----------- ----
2           Even
3           Odd

*/