I have had no problems with modern computers running on faster spec RAM with the RAM running underclocked; however if you haven't already opened the RAM package yet then you should be able to return them for a refund and get the proper 1600Mhz RAM matching the speed of the memory controller. ( * If it were me in this situation, I would probably return the memory and buy the 1600Mhz RAM before opening the memory stick package unless you found a bargain on the 1866Mhz RAM to where the money saved is worth the gamble as to if your system will be picky about the memory being wrong for it. )
I have run 266Mhz and 333Mhz Pentium 4 systems on 400Mhz DDR RAM with the 400Mhz DDR running underclocked with no problems as well as my AMD A8-5545m build that only supports 1333Mhz DDR3 RAM running happily on 1600Mhz DDR3. Only problems I ever had with RAM too fast for a system was with a Celeron 733Mhz that had to run on PC-66 RAM and it didnt run at all on PC-100 or PC-133 RAM and older systems with FSB speed difference or with mismatched latency memory sticks mixed together.
I figured I'd try my A8-5545m desktop running on the 1600Mhz RAM even though it clearly states 1333Mhz DDR3 only supported. I had 8GB of DDR3 RAM ( 2 x 4GB ) left over after a 16GB ( 2 x 8GB ) upgrade of my gaming system left 2 x 4GB 1600Mhz DDR3 sticks available to be passed down to this new low power consumption computer. It was nice being able to just hand-me-down these faster 1600Mhz sticks to this build that calls for 1333Mhz sticks and save money. All memory tests with MEMTEST86 passed as well as I stress tested it and no problems.
However if you were adding the 1866Mhz RAM to 1600Mhz RAM, I would avoid that and only install matched FSB RAM together to avoid instability issues; however I had a system once with PC-100 and PC-133 mixed and the PC-133 down clocked to 100Mhz and no problems including MEMTEST86 passing multiple passes, but I have also seen other times were RAM is sensitive when paired with mismatched speed RAM and BSOD and other issues show and MEMTEST86 when run on the system show many memory issues.
