Yes, you can. But be careful!
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First, you have to use an active adapter, which converts the digital signal of HDMI to an analog signal of VGA.
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Second, your HDMI-VGA adapter needs to be externally powered. We have conducted tests with several HDMI-to-VGA adapters. Adapters that are not powered by some other power source besides the HDMI port behave erratically on the Yodeck Playbox (or Raspberry Pi). They either don't work at all or work for a while and then go on and off constantly. This is because the HDMI port on the Raspberry Pi does not provide enough power to the adapter. Adapters that are externally powered work fine.
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For example, this adapter type does not work properly, but powered adapters have been tested and work. If you are having trouble, try powering the adapter on its own PSU, not from the Yodeck Playbox (or Raspberry Pi) or the TV set. Note that we have not thoroughly tested this type of hardware, and we have no recommendations.