That should work fine. The 6 speed freewheel should fit the frame fine without having to cold set it(which means spreading the frame). The derailleur should have enough travel to add another cog. You will have to adjust your limit screws to make it work. If you were going to an 8 speed or above you would have issues, but your shifters should be able to handle it also. Friction shifters are very easy to work with. Try this link to get some more info.
http://www.sheldonbrown.com/harris/freewheels.html