There are several possible issues.
Instead of "adapters", you need to use converters (with active circuitry).
If either or both "adapters" are bogus adapters (passive devices consisting of wire and connectors), then the connection cannot work.
If the DP connection requires HDCP, and the HDMI-to-VGA converter is of the cheaper variety that doesn't support HDCP, then the connection won't work.
If the DP-to-HDMI converter and/or the HDMI-to-VGA converter do not have external power supplies, then the converters may be starved for power if they try to use line power, and connection won't work.
If you're using a display resolution that the HDMI-to-VGA converter does not support, then the connection won't work. Usually only a subset of 480p, 1024x768, 720p, 1080i and 1080p is supported.
In theory it could work, but you have to use the proper converters and valid resolution.