My two questions are:
Can I use clustered indexes to speed up bulk inserts in big tables?
Never! Imagine another million rows that you need to put in that table and have them physically ordered it is a colossal loss in performance in the long run.
Can I then still efficiently use foreign key relationships if my IDENTITY column is not the clustered index anymore?
Absolutely. By the way, clustered index is no silver bullet and may be slower than your ordinary index.