no, the Vogons couldn't destroy the Earth because it kept popping up in alternate universes... this was mostly because of Arthur, Ford, and Trillian, and their use of the guide...
So the Vogons bought up the Guide, made it into a reverse temporal engineering thingamabob, so it could accomplish a goal of eliminating all of the alternate versions of earth, as well as Arthur, Ford, and Trillian and coincidentally the guide itself.
The guide saw a way to do this, which involved all kinds of stuff that seemed coincidental, but was necessary to get all of them all to the right spot, and have the Grebulons destroy the earth in all it's versions...
it makes perfect sense... if you can think outside of Arthur's frame of reference