Is mortar necessary for a single-row tile baseboard?
You could use construction adhesive, but it takes several days to reach a hardness I'd consider adequate for grouting. You don't want to grout a flexing surface. Also, it'll be more difficult to keep a flat plane among your tiles if you don't use a notched trowel. 

I'd buy some premixed mortar and trowel it onto the wall as you normally would. The outcome will be better, and you'll be able to grout more quickly.