SQLBulkCopy & InMemory tables
It is possible to use an In-Memory Table with the SQLBulkCopy class. I'm not aware of any additional gotchas but did come across this Git Issue in terms of ensuring you properly configure the options of it (depending on the size of your table).
You guys should more importantly understand the differences between an In-Memory Table vs a regular Table, specifically with regards to locks and retry logic for In-Memory Tables being different, which may be important to consider and cause you to make additional changes to your application.
Additional resources for In-Memory Tables:

Microsoft Docs - Memory Optimized Tables

Microsoft Docs - Transactions with Memory Optimized Tables