TTMSFMXGrid Display vs stored precision

Is it possible to store floating points at full precision while displaying rounded values in the cells?

Yes, 


You can use the Floats property to store floating points with full precision and use the Format function property to apply rounding in the OnGetCellData:

procedure TForm1.FormCreate(Sender: TObject);
begin
  TMSFMXGrid1.Floats[1, 1] := 4.123456;
end;

procedure TForm1.TMSFMXGrid1GetCellData(Sender: TObject; ACol, ARow: Integer;
  var CellString: string);
var
  f: Double;
begin
  if TryStrToFloat(CellString, f) then
    CellString := Format('%.0f', [f]);
end;