This should answer your question (the short answer is a "definite maybe" if you set the switch to Mode 2). This customer review is from the Monoprice website for that switch (not amazon):
I bought this specific device because it seems to be designed to overcome a problem with HDMI switches: namely, the HDMI sink determines the type of audio signal sent from the source. In my case, the sink is a brand new Panasonic TC-P55ST30 TV, which claims to support Dolby Digital on its audio output. However, I've read in A/V forums that this typically only applies to internally generated content (i.e., from the tuner), and TVs almost never appear as anything but a stereo device over HDMI. Therefore, an ordinary HDMI switch with audio output will only send PCM audio when the HDMI output is connected to a TV, so you cannot get surround sound encodings such as Dolby Digital or DTS from such a configuration.
THIS device, however, has a set of switches on the back that, according to the manual, sets the mode of the audio output. It can be set to "auto" (Mode 1), meaning it works as other HDMI switches do, allowing the HDMI sink to determine the audio format. It can also be set to force a surround sound format such as Dolby Digital or DTS (Mode 2), or it can be set to force PCM output (Mode 3). The manual warns that in these alternative modes your audio receiver should support the selected format (note: not the HDMI sink, but the audio receiver!). I'm guessing that the mode switch is supposed to spoof the EDID so the switch looks like different types of sinks to the HDMI sources.
Problem solved, right? Not for me. I connect my Sony BDP-S480 Blu-ray player to HDMI input 1, the Panasonic TV to the HDMI output, and the coax audio output to my Sony STR-DE675 receiver which supports Dolby Digital and DTS. (In fact, when I connect the Blu-ray player's audio output directly to the receiver, I get Dolby Digital 5.1.) I set the HDMI switch to Mode 2, but all I get is 2-channel PCM at the receiver. Same for the Toslink output. No matter what mode I set, I get PCM.
So I sent Monoprice technical support a note through their website, and heard nothing within the promised 24 hours. (I eventually got a response three days later.) I started a chat session with them the next day. I chatted with two tech support agents (because the first one got disconnected), but neither one seemed to really understand how this device is supposed to override the audio mode of the HDMI sink, insisting that because my TV only supports stereo I will only ever get PCM output.
Not only does that disagree with the manual and the whole purpose of the device (why have a mode switch?), but it is demonstrably false. Just before I was set to return the switch, I received a replacement Blu-ray player, a Panasonic DMP-BDT210, and I tried the switch out with that. Sure enough, using the Panasonic as a source on the switch produced the correct surround sound at the audio output! In short, the HDMI switch works with the Panasonic player but not the Sony player. So buyers should beware that the switch may or may not work for their particular devices.