Assumng only the first part in your assembly is grounded and everything else is related to it or another part, then yes you can move and rotate the entire assembly.
there are at least 4 ways of doing this :
1. RMB on the first part and select Occurrence Properties. You will be presented with a table showing XYZ position of the part, XYZ rotation and various other parameters.
Simply enter new values of XYZ etc to move and rotate the part to where you want it to be. The value fields will do calculations for you, so if you wanted to move 500mm along positive X direction, just type in +500 after the value that's already there (delete any units characters such as in or mm).
2. Delete the ground constraint and use the move command, the re-apply a ground constraint. Note that if you only SUPRESS the ground constraint, the part will move back to it's original location if you unsuppress it again.
3. Delete the ground constraint and apply relationships between part faces and the base reference planes.
4. Create a co-ordinate system in the part file. Then create one in the assembly file. Now use the match co-ordinate systems option in the assembly to locate the part in the assembly. You can change the positions and orientations of each one as you require.
Hope this helps.
bc.