Is there any reason to have nonclustered indexes on a table with only 1 page in the clustered index?
do the nonclustered indexes even matter?

Yes.  You have multiple copies of this table (or subsets of it), and updates have to be coordinated across all the copies.  Query performance is probably not enhanced by the non-clustered indexes, but they are probably the cause of your deadlocks.
But for SELECT query performance, the non-clustered indexes shouldn't help.