Data compression with in memory OLTP Will having data compression enabled decrease the amount of memory used by an in memory OLTP table? 

If yes I assume the CPU workload will increase.
Looking at the CREATE TABLE definition for 2014 and scrolling down to the box headed "--Memory optimized CREATE TABLE Syntax", there is no mention of compression.  Ergo, compression is not available for in-memory tables.

But yes, compression uses more CPU.  Our experience is that query elapsed times are still shorter because the extra compute time is more than compensated for by the reduced IO latency.

Update: in memory tables now support columnstore indexes which employ compression.