No, space won't be taken twice.
create table test (id int not null primary key, c1 int, c2 int)
create index ix1_test on test (c1)
create index ix2_test on test (c1) include (id)
create index ix3_test on test (c1) include (id, c2)
sp_SQLskills_SQL2012_helpindex shows this information:
index_name index_description index_keys included_columns columns_in_tree columns_in_leaf
[PK__test] clustered, unique, PK [id] NULL [id] All columns "included"
[ix1_test] nonclustered [c1] NULL [c1], [id] [c1], [id]
[ix2_test] nonclustered [c1] [id] [c1], [id] [c1], [id]
[ix3_test] nonclustered [c1] [id], [c2] [c1], [id] [c1], [id], [c2]