Does IR remote work through acrylic glass?
Here's a search result from ePlastics, a reliable plastics manufacturer (companies I have worked for have bought from them repeatedly).


  Infrared transmitting (IRT) sheet was specifically formulated for projects requiring ultraviolet (UV) and visible light blockage while allowing infrared (IR) transmission starting about 750nm. The physical properties of this product are the same as standard extruded sheet and thus the same fabrication techniques apply. What makes this product special is its ability to transmit light in the IR region. We stock this in 0.060" and 0.118".
  
  Note: All plexiglass sheet is infrared transmitting. This grade is
  opaque to visible light and allows infrared light through. Unlike
  glass, you can put all grades of plexiglass in front of DVR's, cable
  boxes, DVD players, etc. and your remote control, wireless router,
  etc. will still work. This particular acrylic material is black and
  only transmits infrared, which makes it ideal for hiding a CCD video
  camera.


While it's probably not safe to say that all acrylics transmit all frequencies of IR light, based on this I would say it's safe to say that most acrylics (and Plexiglas brand specifically) would allow transmission of remote control signals.

The particular result above is for a plastic that is opaque to visible light, but if you're looking for clear, you could probably call them and verify that the clear versions transmit IR light, even if you're not going to buy from them.