The DBID isn't the issue. The issue would be the same DB_NAME being used. You'd have to differentiate the two by using a different DB_UNIQUE_NAME.
Obviously you must
a) first create the parameter file for the new database [specifying a new location for the controlfile !!!!!]
b) restore controlfile
b) use SET NEWNAME to specify the new location of each datafile *before* you RESTORE DATABASE
c) recover using the same archivelogs (having the same DBID)
Hemant K Chitale
I strongly recommend, go for RMAN DUPLICATE ! It will take care of all concerns you raised, even in same cluster/ server !
To prevent overwriting of files, use DB_CREATE_FILE_DEST / DB_FILE_NAME_CONVERT.
Do NOT use non-OMF names (e.g. +DG/control01.ctl) for control files.
If you have combination of non-OMF and OMF file names in source DB, use SET NEWNAME FOR DATAFILE <file#> to '+NEW_DG' for every file.