No setting up a supply line doesn't move the settler.
When you write that the option you get is to set up a supply line does that mean that the option to move is greyed out or not there at all?
To send a settler to a full settlement you boost your charisma just before sending them.
Graqe mentats give a +5 boost i think.
Actually come to think of it I'm not sure if you can send a settler to a settlement that you aren't connected to with a supply line as I've never tried it.
Someone else might know or you could do a hard save and test it out yourself.
For me it's like this in workshop mode.
With the settler highlighted you can command them, move them, or assign them to a supply line.
http://ocau.com/pix/60cyh
When you select move another menu comes up of the available destinations.
for me if a destination is greyed out it's because it's at capacity so i then boost my charisma sufficiently to temporarily overcome the limitation.
Like taking graqe mentats and drinking a brew as my outfit is always the same charisma boosting level. Suit, hat and glasses.