It's a little hard to visualize exactly what you are saying, but, in general terms, no, they can not take over an access easement. It is for the benefit of all property owners, and no one owner can prevent any of the others from using it.
If there is a designated area for driving, such as an obvious dirt or gravel road, and then a grass area flanking it on both sides, then driving on the grass might be a different story. Maybe, maybe not. It would certainly be a non-neighborly thing to do.
Stephen Calder Land Surveyor, not a Lawyer

