I don’t think that there is a way to this with the default Mendix Datagrid on opening the page.
I do believe however that if you open a new page from the grid without closing the page that, if you close the new page or if the user presses the browser back button, the paging and used search of that grid would be still in place.
Another alternative would be to use a listview with custom paging. Then you can manually hold the paging.