It will work but only if it's an Active HDMI-to-VGA adapter (this converts the digital output of HDMI to an analog signal required for VGA input).
You've probably already got an active one since I don't think passive ones exist for HDMI-to-VGA, there'd be no point since they wouldn't work however they were used.
Image quality on the screen may suffer slightly due to the digital-to-analog conversion as opposed to using straight-through analog from an analog source, but I doubt you'll notice it much if the adapter-cable is good quality.
Your PC's "performance" cannot be affected by the type of monitor connection that you use.