If your DBCC checks would fail then chances are your not going to be able to restore the database..at least not cleanly. This is one of the reasons it is good to run DBCC checks prior to a backup.
I too have a database that I can not run a DBCC CHECKDB on. It is a 24x7 300 GB. I am fortunate enough to be able to create a standby database within minutes using a snapshot with exact copies of the files. This is with the EMC TimeFinder utility on a SAN.
Some things you may want to think about is breaking up the DBCC CHECKDB command with the DBCC CHECKALLOC and a DBCC CHECKTABLE statements. I have also read somewhere that these checks can be performed at the filegroup level. If your filegroups are laid out with some granularity it may be possible to run the checks on the database.
Not sure if any of this helps, but thought I would throw a couple of cents in.
"Keep Your Stick On the Ice" ..Red Green