If I follow what you are asking, the answer is yes. We did it by entering 60 Lakes Basin over Rae Col after crossing Glenn Pass and exiting the basin by following the outlet creek of the northern most lake-let in the basin down to the unnamed lake north of Arrowhead (or NW of Dollar). This section is a bit steep but nothing beyond some class 2 scrambling. From there, we followed the inlet creek of the unnamed lake up to Arrowhead Lake. There is actually an old trail that runs directly alongside this creek with switchbacks up to Arrowhead. The switchbacks looked like they had been engineered, so this was at one time probably more than just a use trail. We did not go north from this unnamed lake, but the old trail probably head north to connect with the JMT. You could also exit 60 Lakes Basin by going through "Basin Notch" just to the west of Arrowhead. I think that is the more "traditional" cross country route. If you want, I probably have pics of the cross country sections we did if you want to see them.
BTW, take the time to visit all the little lakes in the basin. Most are quite nice, especially the ones just below Mount Clarence King.