I have driven a 1680x1050 display with a VGA cable, so I imagine it could handle a Blu-Ray or HD-DVD 1920x1080p signal.
However, as Pressure noted, if the content is protected by HDCP (and it should be), since VGA does not support that standard, it will not display the signal at full-resolution (I believe it halves it to 960 x 540).